3sin^2(2x)-sinxcosx=2

Question

3sin^2(2x)-sinxcosx=2

Answer 1

sin2x=2sinxcosx  =>

 

3sin^2(2x)-1/2*sin2x=2

6y^2-y-2=0

y1,2=(1+-7)/2

sin2x=-1/2 => 2x=-pi/6 => x=-pi/12

sin2x=2/3 => x=1/2*arcsin(2/3)