1- cos2 / 1+sin=sin

Question

you need to estalished the identity so that what is the correct answer......

  1-cos2/1+sin=sin

Answer 1

cos(2x)≡1-2sin²(x);

(1-cos(2x))/(1+sin(x))=sin(x),

2sin²(x)/(1+sin(x))=sin(x),

2sin²(x)=sin(x)+sin²(x),

sin²(x)-sin(x)=0,

sin(x)(sin(x)-1)=0, therefore sin(x)=0⇒x=nπ or sin(x)=1⇒x=π/2+2nπ=(4n+1)π/2, where n is an integer (including 0).