Thread: Prove this trigonometric identity

Can somebody show me the steps to prove this question.

Prove that:

cos x + cos x = 2sec x
1 - sin x 1 + sin x

{cosx}/{1-sinx} + {cosx}/{1+sinx} = {(cosx)(1+sinx)+(cosx)(1-sinx)}/{(1-sinx)(1+sinx)}=

={(cosx)(1+sinx)+(cosx)(1-sinx)}/{(1-(sinx)^2}=

={(cosx)(1+sinx)+(cosx)(1-sinx)}/{(cosx)^2}=

={(1+sinx)+(1-sinx)}/{(cosx)}=

={2}/{cosx}=

=2secx

Originally Posted by GAVREED2

Can somebody show me the steps to prove this question.

Prove that:

cos x + cos x = 2sec x
1 - sin x 1 + sin x

working on the left side, get a common denominator ...



... then add the two fractions.