Prove the following trigonometric identity:
(1-sinx)/(cosx)=(cosx)/(1+sinx)
Not so sure how to do this, I have tried converting the "1" into sin^2x+cos^2x but am still confused.

Question

Prove the following trigonometric identity:
(1-sinx)/(cosx)=(cosx)/(1+sinx)
Not so sure how to do this, I have tried converting the "1" into sin^2x+cos^2x but am still confused.

hartnn · Answer

multiply and divide numerator and denominator of left side by 1+ sin x
what u get ?

anonymous · Answer

(1-sinx^2)/(cosx+cosxsinx)?

hartnn · Answer

keep the denominator as cos x (1+sin x)

and from sin^2 x+cos^2 x =1
what will be 1- sin^2 x = ... ?

anonymous · Answer

cos^2x/cosx(1+sinx)

hartnn · Answer

what gets cancelled ?
what remains ?

anonymous · Answer

cosx/(1+sinx)

hartnn · Answer

:)
any doubts ?

anonymous · Answer

Nope thanks for your help once again I just need more practice on these questions :D

hartnn · Answer

yes, keep practicing, then after some time you will be able to solve them mentally, lol :)
welcome ^_^