Trigonometri Contoh

\frac{\tan^{2} (x)}{\sec^{2} (x)} + \frac{\cot^{2} (x)}{\csc^{2} (x)}

$\frac{\tan^{2} (x)}{\sec^{2} (x)} + \frac{\cot^{2} (x)}{\csc^{2} (x)}$

Langkah 1

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 1.1

Tulis kembali

\frac{\tan^{2} (x)}{\sec^{2} (x)}

$\frac{\tan^{2} (x)}{\sec^{2} (x)}$ sebagai

{(\frac{\tan (x)}{\sec (x)})}^{2}

${(\frac{\tan (x)}{\sec (x)})}^{2}$ .

{(\frac{\tan (x)}{\sec (x)})}^{2} + \frac{\cot^{2} (x)}{\csc^{2} (x)}

${(\frac{\tan (x)}{\sec (x)})}^{2} + \frac{\cot^{2} (x)}{\csc^{2} (x)}$

Langkah 1.2

Tulis kembali

\sec (x)

$\sec (x)$ dalam bentuk sinus dan kosinus.

{(\frac{\tan (x)}{\frac{1}{\cos (x)}})}^{2} + \frac{\cot^{2} (x)}{\csc^{2} (x)}

${(\frac{\tan (x)}{\frac{1}{\cos (x)}})}^{2} + \frac{\cot^{2} (x)}{\csc^{2} (x)}$

Langkah 1.3

Tulis kembali

\tan (x)

$\tan (x)$ dalam bentuk sinus dan kosinus.

{(\frac{\frac{\sin (x)}{\cos (x)}}{\frac{1}{\cos (x)}})}^{2} + \frac{\cot^{2} (x)}{\csc^{2} (x)}

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

Langkah 1.4

Kalikan balikan dari pecahan tersebut untuk membagi dengan

\frac{1}{\cos (x)}

$\frac{1}{\cos (x)}$ .

{(\frac{\sin (x)}{\cos (x)} \cos (x))}^{2} + \frac{\cot^{2} (x)}{\csc^{2} (x)}

${(\frac{\sin (x)}{\cos (x)} \cos (x))}^{2} + \frac{\cot^{2} (x)}{\csc^{2} (x)}$

Langkah 1.5

Tulis

\cos (x)

$\cos (x)$ sebagai pecahan dengan penyebut

1

$1$ .

{(\frac{\sin (x)}{\cos (x)} \cdot \frac{\cos (x)}{1})}^{2} + \frac{\cot^{2} (x)}{\csc^{2} (x)}

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

Langkah 1.6

Batalkan faktor persekutuan dari

\cos (x)

$\cos (x)$ .

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Langkah 1.6.1

Batalkan faktor persekutuan.

{(\frac{\sin (x)}{\cos (x)} \cdot \frac{\cos (x)}{1})}^{2} + \frac{\cot^{2} (x)}{\csc^{2} (x)}

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

Langkah 1.6.2

Tulis kembali pernyataannya.

\sin^{2} (x) + \frac{\cot^{2} (x)}{\csc^{2} (x)}

$\sin^{2} (x) + \frac{\cot^{2} (x)}{\csc^{2} (x)}$

\sin^{2} (x) + \frac{\cot^{2} (x)}{\csc^{2} (x)}

$\sin^{2} (x) + \frac{\cot^{2} (x)}{\csc^{2} (x)}$

Langkah 1.7

Tulis kembali

\frac{\cot^{2} (x)}{\csc^{2} (x)}

$\frac{\cot^{2} (x)}{\csc^{2} (x)}$ sebagai

{(\frac{\cot (x)}{\csc (x)})}^{2}

${(\frac{\cot (x)}{\csc (x)})}^{2}$ .

\sin^{2} (x) + {(\frac{\cot (x)}{\csc (x)})}^{2}

$\sin^{2} (x) + {(\frac{\cot (x)}{\csc (x)})}^{2}$

Langkah 1.8

Tulis kembali

\csc (x)

$\csc (x)$ dalam bentuk sinus dan kosinus.

\sin^{2} (x) + {(\frac{\cot (x)}{\frac{1}{\sin (x)}})}^{2}

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

Langkah 1.9

Tulis kembali

\cot (x)

$\cot (x)$ dalam bentuk sinus dan kosinus.

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

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

Langkah 1.10

Kalikan balikan dari pecahan tersebut untuk membagi dengan

\frac{1}{\sin (x)}

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

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

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

Langkah 1.11

Tulis

\sin (x)

$\sin (x)$ sebagai pecahan dengan penyebut

1

$1$ .

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

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

Langkah 1.12

Batalkan faktor persekutuan dari

\sin (x)

$\sin (x)$ .

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Langkah 1.12.1

Batalkan faktor persekutuan.

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

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

Langkah 1.12.2

Tulis kembali pernyataannya.

\sin^{2} (x) + \cos^{2} (x)

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

\sin^{2} (x) + \cos^{2} (x)

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

\sin^{2} (x) + \cos^{2} (x)

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

Langkah 2

Terapkan identitas pythagoras.

1

$1$