Question

1+cos x+sin x/1+cos x-sin x = 1+sin x/cos x.
prove this

Answer 1

Given,

(1+cos x+sin x)/(1+cos x-sin x )
multiplying with conjugate of denominator.
→
(1+cos x+sin x)²/(1+cos x-sin x )((1+cos x+sin x)
→(1+cos x+sin x)²/{(1+cosx)² - sin²x

see picture!.
use following identities:-
sin²x +cos²x= 1
1-sin²x= cos²x..
Hope it helped you!.

Answer 2

you can see your answer