Question

prove the identity: (1+cosx)(cox+sinx-1)=(sinx)(cosx-sinx+1)

Answer 1

(1+cosx)(cox+sinx-1) =
1(cox+sinx-1) + cos x (cox+sinx-1)
=cos x+ sin x -1 + cos^2 x +cos x sin x -cos x

cos x cancel
= sinx -1 +cos ^2x +cos x sin x
= sin x -(1-cos^2x) +cos x sin x

= sin x - sin ^2x + cos x sin x
now factor sin x
= sin x (1-sin x + cos x ) it is rs