Помогите решить cos2x+3=6sinx*cosx

Question

Помогите решить cos2x+3=6sinx*cosx

Answer 1

Cos²x-sin²x+3cos²x+3sin²x-6sinxcosx=0/cos²x
2tg²x-6tgx+4=0
tgx=a
a²-3a+2=0
a1=a2=3 U a1*a2=2
a1=1⇒tgx=1⇒x=π/4+πn,n∈z
a2=2⇒tgz=2⇒x=arctg2+πk,k∈z