2sin2x/ctgx+3cos^2 x=1-2cosx

Question

2sin2x/ctgx+3cos^2 x=1-2cosx

Answer 1

4sinxcosx *sinx/cosx  +3cos²x-1+2cosx=0
4sin²x+3cos²x-1+2cosx=0
4-4cos²x+3cos²x-1+2cosx=0
cos²x-2cosx-3=0
cosx=a
a²-2a-3=0
a1+a2=2 U a1*a2=-3
a1=3⇒cosx=3∉[-1;1]-нет решения
a2=-1⇒cosx=-1⇒x=π+2πn