Sin2x+cosx+2sinx=-1.

Question

Sin2x+cosx+2sinx=-1.

Answer 1

2sinx(cosx+1)+(cosx+1)=0
(cosx+1)(2sinx+1)=0
cosx=-1⇒x=π+2πn,n∈z
sinx=-1/2⇒x=(-1)^(k+1)*π/6+πk,k∈z