Question

2cos²x=√3sin(1,5Π+x)

Answer 1

$2cos^2x= sqrt{3} sin(1.5 pi +x)\ \ 2cos^2x=-sqrt{3} cos x\ \ 2cos^2x+sqrt{3} cos x=0 \ \ cos x(2cos x+sqrt{3} )=0\ \ left[begin{array}{ccc}cos x=0\ cos x=- frac{sqrt{3} }{2} end{array}right~~~~~Rightarrow~~~~~~~ left[begin{array}{ccc}x_1= frac{pi}{2}+ pi n,n in mathbb{Z}\ x_2=pm frac{5 pi }{6} +2 pi n,n in mathbb{Z} end{array}right$