secx+tanx/secx- tanx = 1+2sinx+sin^2x/ cos^2x

Answer 1

I will assume you want to prove the identity to be true.
The way you typed , the statement is NOT an identity
You must have meant:
(secx+tanx)/(secx- tanx) = (1+2sinx+sin^2x)/ cos^2x

LS = (1/cosx + sinx/cosx) / (1/cosx - sinx/cosx)
= ( (1+sinx)/cosx)/( (1-sinx)/cosx)
= (1+sinx) / (1 - sinx)

RS = (1+sinx)^2 / (1 - sin^2 x)
= (1+sinx)(1+sinx)/( (1-sinx)(1+sinx))
= (1+sinx)/(1-sinx)
= LS