Тригонометрия (2cos^2)x=1-sinx

Question

Тригонометрия
(2cos^2)x=1-sinx

Answer 1

2-2sin²x-1+sinx=0
sinx=a
2a²-a-1=0
D=1+8=9
a1=(1-3)/4=-1/2⇒sinx=-1/2⇒x=(-1)^(n+1)*π/6+πn,n∈z
a2=(1+3)/4=1⇒sinx=1⇒x=π/2+2πk,k∈z