Question

$5sin2x+5cosx-8sinx-4=0$

Answer 1

10sinxcosx+5cosx-8sinx-4=0
5cosx(2sinx+1)-4(2sinx+1)=0
(2sinx+1)(5cosx-4)=0
2sinx+1=0
sinx=-1/2
x=(-1)^(n+1)*π/6+πn,n∈z
2cosx-4=0
cosx=0,8
x=+-arccos0,8+2πk,k∈z