Решите уравнение sin^4x-cos^4x+2cos^2x=cos2x

Question

Решите уравнение sin^4x-cos^4x+2cos^2x=cos2x

Answer 1

(sin^2x + cos^2x)(sin^2x - cos^2x) = cos2x - 2cos^2x
sin^2x - cos^2x = cos^2x - sin^2x - 2cos^2x = - 1
1 - cos^2x - cos^2x = - 1    ->  cos^2x = 1   -> 
cosx = 1  или  cosx = - 1   ->  x = πn   n ∈ Z