Precalculus - Trigonometric Identities and Equations (Proving)

Proof of trigonometric identities:
a) 1/(tanx+secx)=(1-sin⁡x)/cosx
b) (sinx+cos⁡x)(1-sin⁡xcosx)=sin^3⁡x+cos^3⁡x
c) cos⁡2x/(1+sin⁡2x)=(cotx-1)/(cotx+1)