Prove the identities sinx/1 + cosx =1-cosx/sinx

Question

Please help

Answer 1

sin x/(1+cos x) = (1-cos x)/sin x

 

sin x = (1+cos x)(1-cos x)/sin x

sin x = (1 - cos² x)/sin x

 

Use the Pythagorean Identity sin² x + cos² x = 1, so sin² x = 1-cos² x

 

sin x = sin² x/sin x

sin x = sin x

 

QED