Question

1. cotan x - cos x/cotan x = cos² x / 1+sin x
2. cosec x + tan x + cotan x = cos x +1/sin x cos x
3. tan x/1-tan² x= sin x cos x/ cos² x- sin² x
4.sin² x/1-cos x=1 + cos x
5. (1+ cos x)² - (1- cos x)² = 4 cos x
bantuin membuktikan identitas trigonometri diatas , saya masih kesulitan.

Answer 1

2. = ( \frac{1}{sin x} + \frac{cos x }{sin x} ) + \frac{sin x}{cos x} [/tex] 
= \frac{1 + cos x }{sin x} + \frac{sin x}{cos x} [/tex] 
 = \frac{(1 + cos x ) cos x + sin^2x}{sin x cos x} [/tex]
=  \frac{cos x + cos^2 + sin^2 x}{sin x cos x} [/tex] 
= \frac{cos x +1}{sin x cos x} [/tex]