Cos 2 x - cos x * sin x = 0

Question

Cos 2 x - cos x * sin x = 0

Answer 1

Cos²x-sin²x-cosxsinx=0/cos²x
tg²x+tgx-1=0
tgx=a
a²+a-1=0
D=1+4=5
a1=(-1-√5)/2⇒tgx=(-1-√5)/2⇒x=-arctg(1+√5)/2+πn,n∈z
a2=(-1+√5)/2⇒tgx=(√5-1)/2⇒x=arctg(√5-1)/2+πk,k∈z