Cos ^2 x-12 cos x sin x=13sin^2 x п

Question

Cos ^2 x-12 cos x sin x=13sin^2 x п

Answer 1

Cos²x-12cosxsinx-13sin²x=0 | :cos²x
1-12tgx-13tg²x=0
13tg²x+12tgx-1=0
(tgx+1)(13tgx-1)=0
tgx=-1
tgx=1/13
x1=-П/4+Пn, n€Z
x2=arctg(1/13)+Пk, k€Z