Question

Establish the identity.

sinx + cosx/sinx - cosx = 1+2sinxcosx/2sin^2x-1

Answer 1

Do you mean
(sinx + cosx)/(sinx - cosx) = (1+2sinxcosx)/(2sin^2x-1 ) ?????????
If so then
[(sinx + cosx)/(sinx - cosx)][(sinx+cosx)/(sinx + cosx)]

= [sinx + cosx]^2/[sin^2x-cos^2x]

= [1 + 2 sin x cos x] / [sin^2x - (1-sin^2x)]

= [1 + 2 sin x cos x] / [2 sin^2 x - 1]