Question

How do you prove that `(cos^2x)/(1 + sin2x) = (1 - tanx)/(1+ tanx)`?

Answer 1

Your identity is false!

Explanation:

`cos^2x/(1 + 2sinxcosx) = (1 - sinx/cosx)/(1 + sinx/cosx)`

`= ((cosx - sinx)/cosx)/((cosx + sinx)/cosx)`

`= (cosx - sinx)/(cosx + sinx)`

Your identity is false, since the left side does not equal the right!!