Trigonometri Contoh

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

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

Langkah 1

Tulis kembali

1

$1$ sebagai

1^{2}

$1^{2}$ .

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

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

Langkah 2

Tulis kembali

(\cos (x) + \sin (x)) (\cos (x) + \sin (x))

$(\cos (x) + \sin (x)) (\cos (x) + \sin (x))$ sebagai

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

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

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

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

Langkah 3

Karena kedua suku merupakan kuadrat sempurna, faktorkan menggunakan rumus beda pangkat dua,

a^{2} - b^{2} = (a + b) (a - b)

$a^{2} - b^{2} = (a + b) (a - b)$ di mana

a = 1

$a = 1$ dan

b = \cos (x) + \sin (x)

$b = \cos (x) + \sin (x)$ .

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

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

Langkah 4

Terapkan sifat distributif.

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

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