Question

cos2x-2sinx-1=0

Answer 1

$cos2x-2sinx-1=0 \ cos2x=cos^2x-sin^2x=1-2sin^2x \ 1-2sin^2x-2sinx-1=0 \ -2sin^2x-2sinx=0 \ |:(-2) \ sin^2x+sinx=0 \ sinx(sinx+1)=0 \ sinx=0 iff x=kpi,kin Z \ sinx+1=0 iff sinx=-1 iff x= frac{3}{2}pi +2npi,n in Z$

Answer 2

1-2sin²x-2sinx-1=0
-2sinx(sinx+1)=0
sinx=0⇒x=πn
sinx=-1⇒x=-π/2+2πn