Trigonometria Exemplos

$\frac{1 - \sec (x)}{\tan (x)} - \frac{\tan (x)}{1 - \sec (x)} = 2 \cot (x)$

Etapa 1

Comece do lado esquerdo.

$\frac{1 - \sec (x)}{\tan (x)} - \frac{\tan (x)}{1 - \sec (x)}$

Etapa 2

Multiplique $\frac{\tan (x)}{1 - \sec (x)}$ por $\frac{1 + \sec (x)}{1 + \sec (x)}$ .

$\frac{1 - \sec (x)}{\tan (x)} - (\frac{\tan (x)}{1 - \sec (x)} \cdot \frac{1 + \sec (x)}{1 + \sec (x)})$

Etapa 3

Combine.

$\frac{1 - \sec (x)}{\tan (x)} - \frac{\tan (x) (1 + \sec (x))}{(1 - \sec (x)) (1 + \sec (x))}$

Etapa 4

Simplifique o numerador.

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Etapa 4.1

Aplique a propriedade distributiva.

$\frac{1 - \sec (x)}{\tan (x)} - \frac{\tan (x) \cdot 1 + \tan (x) \sec (x)}{(1 - \sec (x)) (1 + \sec (x))}$

Etapa 4.2

Multiplique $\tan (x)$ por $1$ .

$\frac{1 - \sec (x)}{\tan (x)} - \frac{\tan (x) + \tan (x) \sec (x)}{(1 - \sec (x)) (1 + \sec (x))}$

Etapa 5

Simplifique o denominador.

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Etapa 5.1

Expanda $(1 - \sec (x)) (1 + \sec (x))$ usando o método FOIL.

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Etapa 5.1.1

Aplique a propriedade distributiva.

$\frac{1 - \sec (x)}{\tan (x)} - \frac{\tan (x) + \tan (x) \sec (x)}{1 (1 + \sec (x)) - \sec (x) (1 + \sec (x))}$

Etapa 5.1.2

Aplique a propriedade distributiva.

$\frac{1 - \sec (x)}{\tan (x)} - \frac{\tan (x) + \tan (x) \sec (x)}{1 \cdot 1 + 1 \sec (x) - \sec (x) (1 + \sec (x))}$

Etapa 5.1.3

Aplique a propriedade distributiva.

$\frac{1 - \sec (x)}{\tan (x)} - \frac{\tan (x) + \tan (x) \sec (x)}{1 \cdot 1 + 1 \sec (x) - \sec (x) \cdot 1 - \sec (x) \sec (x)}$

Etapa 5.2

Simplifique e combine termos semelhantes.

$\frac{1 - \sec (x)}{\tan (x)} - \frac{\tan (x) + \tan (x) \sec (x)}{1 - \sec^{2} (x)}$

Etapa 6

Escreva $- 1$ como uma fração com denominador $1$ .

$\frac{1 - \sec (x)}{\tan (x)} + \frac{- 1}{1} \cdot \frac{\tan (x) + \tan (x) \sec (x)}{1 - \sec^{2} (x)}$

Etapa 7

Combine.

$\frac{1 - \sec (x)}{\tan (x)} + \frac{- (\tan (x) + \tan (x) \sec (x))}{1 (1 - \sec^{2} (x))}$

Etapa 8

Aplique a propriedade distributiva.

$\frac{1 - \sec (x)}{\tan (x)} + \frac{- \tan (x) - \tan (x) \sec (x)}{1 (1 - \sec^{2} (x))}$

Etapa 9

Multiplique $1 - {\sec (x)}^{2}$ por $1$ .

$\frac{1 - \sec (x)}{\tan (x)} + \frac{- \tan (x) - \tan (x) \sec (x)}{1 - \sec^{2} (x)}$

Etapa 10

Aplique a identidade trigonométrica fundamental.

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Etapa 10.1

Reordene $1$ e $- \sec^{2} (x)$ .

$\frac{1 - \sec (x)}{\tan (x)} + \frac{- \tan (x) - \tan (x) \sec (x)}{- \sec^{2} (x) + 1}$

Etapa 10.2

Fatore $- 1$ de $- \sec^{2} (x)$ .

$\frac{1 - \sec (x)}{\tan (x)} + \frac{- \tan (x) - \tan (x) \sec (x)}{- (\sec^{2} (x)) + 1}$

Etapa 10.3

Reescreva $1$ como $- 1 (- 1)$ .

$\frac{1 - \sec (x)}{\tan (x)} + \frac{- \tan (x) - \tan (x) \sec (x)}{- \sec^{2} (x) - 1 \cdot - 1}$

Etapa 10.4

Fatore $- 1$ de $- \sec^{2} (x) - 1 \cdot - 1$ .

$\frac{1 - \sec (x)}{\tan (x)} + \frac{- \tan (x) - \tan (x) \sec (x)}{- (\sec^{2} (x) - 1)}$

Etapa 10.5

Aplique a identidade trigonométrica fundamental.

$\frac{1 - \sec (x)}{\tan (x)} + \frac{- \tan (x) - \tan (x) \sec (x)}{- \tan^{2} (x)}$

Etapa 11

Converta em senos e cossenos.

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Etapa 11.1

Aplique a identidade recíproca a $\sec (x)$ .

$\frac{1 - \frac{1}{\cos (x)}}{\tan (x)} + \frac{- \tan (x) - \tan (x) \sec (x)}{- \tan^{2} (x)}$

Etapa 11.2

Escreva $\tan (x)$ nos senos e cossenos usando a fórmula do quociente.

$\frac{1 - \frac{1}{\cos (x)}}{\frac{\sin (x)}{\cos (x)}} + \frac{- \tan (x) - \tan (x) \sec (x)}{- \tan^{2} (x)}$

Etapa 11.3

Escreva $\tan (x)$ nos senos e cossenos usando a fórmula do quociente.

$\frac{1 - \frac{1}{\cos (x)}}{\frac{\sin (x)}{\cos (x)}} + \frac{- \frac{\sin (x)}{\cos (x)} - \tan (x) \sec (x)}{- \tan^{2} (x)}$

Etapa 11.4

Escreva $\tan (x)$ nos senos e cossenos usando a fórmula do quociente.

$\frac{1 - \frac{1}{\cos (x)}}{\frac{\sin (x)}{\cos (x)}} + \frac{- \frac{\sin (x)}{\cos (x)} - \frac{\sin (x)}{\cos (x)} \sec (x)}{- \tan^{2} (x)}$

Etapa 11.5

Aplique a identidade recíproca a $\sec (x)$ .

$\frac{1 - \frac{1}{\cos (x)}}{\frac{\sin (x)}{\cos (x)}} + \frac{- \frac{\sin (x)}{\cos (x)} - \frac{\sin (x)}{\cos (x)} \cdot \frac{1}{\cos (x)}}{- \tan^{2} (x)}$

Etapa 11.6

Escreva $\tan (x)$ nos senos e cossenos usando a fórmula do quociente.

$\frac{1 - \frac{1}{\cos (x)}}{\frac{\sin (x)}{\cos (x)}} + \frac{- \frac{\sin (x)}{\cos (x)} - \frac{\sin (x)}{\cos (x)} \cdot \frac{1}{\cos (x)}}{- {(\frac{\sin (x)}{\cos (x)})}^{2}}$

Etapa 11.7

Aplique a regra do produto a $\frac{\sin (x)}{\cos (x)}$ .

$\frac{1 - \frac{1}{\cos (x)}}{\frac{\sin (x)}{\cos (x)}} + \frac{- \frac{\sin (x)}{\cos (x)} - \frac{\sin (x)}{\cos (x)} \cdot \frac{1}{\cos (x)}}{- \frac{\sin^{2} (x)}{\cos^{2} (x)}}$

Etapa 12

Simplifique.

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Etapa 12.1

Reordene os fatores de $- \frac{\sin (x)}{\cos (x)} \cdot \frac{1}{\cos (x)}$ .

$\frac{1 - \frac{1}{\cos (x)}}{\frac{\sin (x)}{\cos (x)}} + \frac{- \frac{\sin (x)}{\cos (x)} - \frac{1}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)}}{- \frac{{\sin (x)}^{2}}{{\cos (x)}^{2}}}$

Etapa 12.2

Para escrever $- \frac{1}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)}$ como fração com um denominador comum, multiplique por $\frac{\cos (x)}{\cos (x)}$ .

$\frac{1 - \frac{1}{\cos (x)}}{\frac{\sin (x)}{\cos (x)}} + \frac{- \frac{\sin (x)}{\cos (x)} - \frac{1}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} \cdot \frac{\cos (x)}{\cos (x)}}{- \frac{{\sin (x)}^{2}}{{\cos (x)}^{2}}}$

Etapa 12.3

Combine $- \frac{1}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)}$ e $\frac{\cos (x)}{\cos (x)}$ .

$\frac{1 - \frac{1}{\cos (x)}}{\frac{\sin (x)}{\cos (x)}} + \frac{- \frac{\sin (x)}{\cos (x)} + \frac{- \frac{1}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} \cos (x)}{\cos (x)}}{- \frac{{\sin (x)}^{2}}{{\cos (x)}^{2}}}$

Etapa 12.4

Combine os numeradores em relação ao denominador comum.

$\frac{1 - \frac{1}{\cos (x)}}{\frac{\sin (x)}{\cos (x)}} + \frac{\frac{- \sin (x) - \frac{1}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} \cos (x)}{\cos (x)}}{- \frac{{\sin (x)}^{2}}{{\cos (x)}^{2}}}$

Etapa 12.5

Simplifique cada termo.

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Etapa 12.5.1

Multiplique o numerador pelo inverso do denominador.

$(1 - \frac{1}{\cos (x)}) \frac{\cos (x)}{\sin (x)} + \frac{\frac{- \sin (x) - \frac{1}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} \cos (x)}{\cos (x)}}{- \frac{{\sin (x)}^{2}}{{\cos (x)}^{2}}}$

Etapa 12.5.2

Aplique a propriedade distributiva.

$1 \frac{\cos (x)}{\sin (x)} - \frac{1}{\cos (x)} \cdot \frac{\cos (x)}{\sin (x)} + \frac{\frac{- \sin (x) - \frac{1}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} \cos (x)}{\cos (x)}}{- \frac{{\sin (x)}^{2}}{{\cos (x)}^{2}}}$

Etapa 12.5.3

Multiplique $\frac{\cos (x)}{\sin (x)}$ por $1$ .

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\cos (x)} \cdot \frac{\cos (x)}{\sin (x)} + \frac{\frac{- \sin (x) - \frac{1}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} \cos (x)}{\cos (x)}}{- \frac{{\sin (x)}^{2}}{{\cos (x)}^{2}}}$

Etapa 12.5.4

Cancele o fator comum de $\cos (x)$ .

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Etapa 12.5.4.1

Mova o negativo de maior ordem em $- \frac{1}{\cos (x)}$ para o numerador.

$\frac{\cos (x)}{\sin (x)} + \frac{- 1}{\cos (x)} \cdot \frac{\cos (x)}{\sin (x)} + \frac{\frac{- \sin (x) - \frac{1}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} \cos (x)}{\cos (x)}}{- \frac{{\sin (x)}^{2}}{{\cos (x)}^{2}}}$

Etapa 12.5.4.2

Cancele o fator comum.

Etapa 12.5.4.3

Reescreva a expressão.

$\frac{\cos (x)}{\sin (x)} - 1 \frac{1}{\sin (x)} + \frac{\frac{- \sin (x) - \frac{1}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} \cos (x)}{\cos (x)}}{- \frac{{\sin (x)}^{2}}{{\cos (x)}^{2}}}$

Etapa 12.5.5

Reescreva $- 1 \frac{1}{\sin (x)}$ como $- \frac{1}{\sin (x)}$ .

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + \frac{\frac{- \sin (x) - \frac{1}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} \cos (x)}{\cos (x)}}{- \frac{{\sin (x)}^{2}}{{\cos (x)}^{2}}}$

Etapa 12.5.6

Multiplique o numerador pelo inverso do denominador.

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + \frac{- \sin (x) - \frac{1}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} \cos (x)}{\cos (x)} (- \frac{{\cos (x)}^{2}}{{\sin (x)}^{2}})$

Etapa 12.5.7

Cancele o fator comum de $\cos (x)$ .

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Etapa 12.5.7.1

Mova o negativo de maior ordem em $- \frac{{\cos (x)}^{2}}{{\sin (x)}^{2}}$ para o numerador.

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + \frac{- \sin (x) - \frac{1}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} \cos (x)}{\cos (x)} \cdot \frac{- {\cos (x)}^{2}}{{\sin (x)}^{2}}$

Etapa 12.5.7.2

Fatore $\cos (x)$ de $- {\cos (x)}^{2}$ .

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + \frac{- \sin (x) - \frac{1}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} \cos (x)}{\cos (x)} \cdot \frac{\cos (x) (- \cos (x))}{{\sin (x)}^{2}}$

Etapa 12.5.7.3

Cancele o fator comum.

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + \frac{- \sin (x) - \frac{1}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} \cos (x)}{\cos (x)} \cdot \frac{\cos (x) (- \cos (x))}{{\sin (x)}^{2}}$

Etapa 12.5.7.4

Reescreva a expressão.

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + (- \sin (x) - \frac{1}{\cos (x)} \cdot \frac{\sin (x)}{\cos (x)} \cos (x)) \frac{- \cos (x)}{{\sin (x)}^{2}}$

Etapa 12.5.8

Multiplique $\frac{\sin (x)}{\cos (x)}$ por $\frac{1}{\cos (x)}$ .

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + (- \sin (x) - \frac{\sin (x)}{\cos (x) \cos (x)} \cos (x)) \frac{- \cos (x)}{{\sin (x)}^{2}}$

Etapa 12.5.9

Eleve $\cos (x)$ à potência de $1$ .

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + (- \sin (x) - \frac{\sin (x)}{{\cos (x)}^{1} \cos (x)} \cos (x)) \frac{- \cos (x)}{{\sin (x)}^{2}}$

Etapa 12.5.10

Eleve $\cos (x)$ à potência de $1$ .

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + (- \sin (x) - \frac{\sin (x)}{{\cos (x)}^{1} {\cos (x)}^{1}} \cos (x)) \frac{- \cos (x)}{{\sin (x)}^{2}}$

Etapa 12.5.11

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + (- \sin (x) - \frac{\sin (x)}{{\cos (x)}^{1 + 1}} \cos (x)) \frac{- \cos (x)}{{\sin (x)}^{2}}$

Etapa 12.5.12

Some $1$ e $1$ .

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + (- \sin (x) - \frac{\sin (x)}{{\cos (x)}^{2}} \cos (x)) \frac{- \cos (x)}{{\sin (x)}^{2}}$

Etapa 12.5.13

Combine $\cos (x)$ e $\frac{\sin (x)}{{\cos (x)}^{2}}$ .

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + (- \sin (x) - \frac{\cos (x) \sin (x)}{{\cos (x)}^{2}}) \frac{- \cos (x)}{{\sin (x)}^{2}}$

Etapa 12.5.14

Cancele o fator comum de $\cos (x)$ e ${\cos (x)}^{2}$ .

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Etapa 12.5.14.1

Fatore $\cos (x)$ de $\cos (x) \sin (x)$ .

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + (- \sin (x) - \frac{\cos (x) (\sin (x))}{{\cos (x)}^{2}}) \frac{- \cos (x)}{{\sin (x)}^{2}}$

Etapa 12.5.14.2

Cancele os fatores comuns.

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Etapa 12.5.14.2.1

Fatore $\cos (x)$ de ${\cos (x)}^{2}$ .

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + (- \sin (x) - \frac{\cos (x) (\sin (x))}{\cos (x) \cos (x)}) \frac{- \cos (x)}{{\sin (x)}^{2}}$

Etapa 12.5.14.2.2

Cancele o fator comum.

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + (- \sin (x) - \frac{\cos (x) \sin (x)}{\cos (x) \cos (x)}) \frac{- \cos (x)}{{\sin (x)}^{2}}$

Etapa 12.5.14.2.3

Reescreva a expressão.

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + (- \sin (x) - \frac{\sin (x)}{\cos (x)}) \frac{- \cos (x)}{{\sin (x)}^{2}}$

Etapa 12.5.15

Mova o número negativo para a frente da fração.

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + (- \sin (x) - \frac{\sin (x)}{\cos (x)}) (- \frac{\cos (x)}{{\sin (x)}^{2}})$

Etapa 12.5.16

Aplique a propriedade distributiva.

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} - \sin (x) (- \frac{\cos (x)}{{\sin (x)}^{2}}) - \frac{\sin (x)}{\cos (x)} (- \frac{\cos (x)}{{\sin (x)}^{2}})$

Etapa 12.5.17

Cancele o fator comum de $\sin (x)$ .

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Etapa 12.5.17.1

Mova o negativo de maior ordem em $- \frac{\cos (x)}{{\sin (x)}^{2}}$ para o numerador.

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} - \sin (x) \frac{- \cos (x)}{{\sin (x)}^{2}} - \frac{\sin (x)}{\cos (x)} (- \frac{\cos (x)}{{\sin (x)}^{2}})$

Etapa 12.5.17.2

Fatore $\sin (x)$ de $- \sin (x)$ .

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + \sin (x) \cdot - 1 \frac{- \cos (x)}{{\sin (x)}^{2}} - \frac{\sin (x)}{\cos (x)} (- \frac{\cos (x)}{{\sin (x)}^{2}})$

Etapa 12.5.17.3

Fatore $\sin (x)$ de ${\sin (x)}^{2}$ .

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + \sin (x) \cdot - 1 \frac{- \cos (x)}{\sin (x) \sin (x)} - \frac{\sin (x)}{\cos (x)} (- \frac{\cos (x)}{{\sin (x)}^{2}})$

Etapa 12.5.17.4

Cancele o fator comum.

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + \sin (x) \cdot - 1 \frac{- \cos (x)}{\sin (x) \sin (x)} - \frac{\sin (x)}{\cos (x)} (- \frac{\cos (x)}{{\sin (x)}^{2}})$

Etapa 12.5.17.5

Reescreva a expressão.

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} - 1 \frac{- \cos (x)}{\sin (x)} - \frac{\sin (x)}{\cos (x)} (- \frac{\cos (x)}{{\sin (x)}^{2}})$

Etapa 12.5.18

Cancele o fator comum de $\sin (x)$ .

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Etapa 12.5.18.1

Mova o negativo de maior ordem em $- \frac{\sin (x)}{\cos (x)}$ para o numerador.

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} - 1 \frac{- \cos (x)}{\sin (x)} + \frac{- \sin (x)}{\cos (x)} (- \frac{\cos (x)}{{\sin (x)}^{2}})$

Etapa 12.5.18.2

Mova o negativo de maior ordem em $- \frac{\cos (x)}{{\sin (x)}^{2}}$ para o numerador.

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} - 1 \frac{- \cos (x)}{\sin (x)} + \frac{- \sin (x)}{\cos (x)} \cdot \frac{- \cos (x)}{{\sin (x)}^{2}}$

Etapa 12.5.18.3

Fatore $\sin (x)$ de $- \sin (x)$ .

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} - 1 \frac{- \cos (x)}{\sin (x)} + \frac{\sin (x) \cdot - 1}{\cos (x)} \cdot \frac{- \cos (x)}{{\sin (x)}^{2}}$

Etapa 12.5.18.4

Fatore $\sin (x)$ de ${\sin (x)}^{2}$ .

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} - 1 \frac{- \cos (x)}{\sin (x)} + \frac{\sin (x) \cdot - 1}{\cos (x)} \cdot \frac{- \cos (x)}{\sin (x) \sin (x)}$

Etapa 12.5.18.5

Cancele o fator comum.

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} - 1 \frac{- \cos (x)}{\sin (x)} + \frac{\sin (x) \cdot - 1}{\cos (x)} \cdot \frac{- \cos (x)}{\sin (x) \sin (x)}$

Etapa 12.5.18.6

Reescreva a expressão.

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} - 1 \frac{- \cos (x)}{\sin (x)} + \frac{- 1}{\cos (x)} \cdot \frac{- \cos (x)}{\sin (x)}$

Etapa 12.5.19

Cancele o fator comum de $\cos (x)$ .

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Etapa 12.5.19.1

Fatore $\cos (x)$ de $- \cos (x)$ .

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} - 1 \frac{- \cos (x)}{\sin (x)} + \frac{- 1}{\cos (x)} \cdot \frac{\cos (x) \cdot - 1}{\sin (x)}$

Etapa 12.5.19.2

Cancele o fator comum.

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} - 1 \frac{- \cos (x)}{\sin (x)} + \frac{- 1}{\cos (x)} \cdot \frac{\cos (x) \cdot - 1}{\sin (x)}$

Etapa 12.5.19.3

Reescreva a expressão.

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} - 1 \frac{- \cos (x)}{\sin (x)} - 1 \frac{- 1}{\sin (x)}$

Etapa 12.5.20

Simplifique cada termo.

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Etapa 12.5.20.1

Mova o número negativo para a frente da fração.

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} - 1 (- \frac{\cos (x)}{\sin (x)}) - 1 \frac{- 1}{\sin (x)}$

Etapa 12.5.20.2

Multiplique $- 1 (- \frac{\cos (x)}{\sin (x)})$ .

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Etapa 12.5.20.2.1

Multiplique $- 1$ por $- 1$ .

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + 1 \frac{\cos (x)}{\sin (x)} - 1 \frac{- 1}{\sin (x)}$

Etapa 12.5.20.2.2

Multiplique $\frac{\cos (x)}{\sin (x)}$ por $1$ .

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + \frac{\cos (x)}{\sin (x)} - 1 \frac{- 1}{\sin (x)}$

Etapa 12.5.20.3

Mova o número negativo para a frente da fração.

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + \frac{\cos (x)}{\sin (x)} - 1 (- \frac{1}{\sin (x)})$

Etapa 12.5.20.4

Multiplique $- 1 (- \frac{1}{\sin (x)})$ .

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Etapa 12.5.20.4.1

Multiplique $- 1$ por $- 1$ .

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + \frac{\cos (x)}{\sin (x)} + 1 \frac{1}{\sin (x)}$

Etapa 12.5.20.4.2

Multiplique $\frac{1}{\sin (x)}$ por $1$ .

$\frac{\cos (x)}{\sin (x)} - \frac{1}{\sin (x)} + \frac{\cos (x)}{\sin (x)} + \frac{1}{\sin (x)}$

Etapa 12.6

Combine os numeradores em relação ao denominador comum.

$\frac{\cos (x) - 1 + \cos (x) + 1}{\sin (x)}$

Etapa 12.7

Some $\cos (x)$ e $\cos (x)$ .

$\frac{2 \cos (x) - 1 + 1}{\sin (x)}$

Etapa 12.8

Some $- 1$ e $1$ .

$\frac{2 \cos (x) + 0}{\sin (x)}$

Etapa 12.9

Some $2 \cos (x)$ e $0$ .

$\frac{2 \cos (x)}{\sin (x)}$

Etapa 13

Reescreva $\frac{2 \cos (x)}{\sin (x)}$ como $2 \cot (x)$ .

$2 \cot (x)$

Etapa 14

Como os dois lados demonstraram ser equivalentes, a equação é uma identidade.

$\frac{1 - \sec (x)}{\tan (x)} - \frac{\tan (x)}{1 - \sec (x)} = 2 \cot (x)$ é uma identidade