Sin^2(3x)-cos^2(3x)=1

Question

Sin^2(3x)-cos^2(3x)=1

Answer 1

sin^2(3x) - cos^2(3x) =1

косинус двойного аргумента
cos2a = cos^2(a) - sin^2(a)
- (cos^2(3x) - sin^2(3x)) = 1
- cos(2*3x) = 1
- cos6x = 1
cos6x = - 1
6x = pi + 2pik  /:6
x = pi/6 + pik/3 , k ∈ Z