Sin^4 x*Cos^2 x-Cos^4 x *Sin^2 x= Cos2x

Question

Sin^4 x*Cos^2 x-Cos^4 x *Sin^2 x= Cos2x

Answer 1

Sin(x)^4 cos(x)^2 - cos(x)^4 sin(x)^2 = cos(2x)
sin(x)^2 cos(x)^2 [ sin(x)^2 - cos(x)^2 ] = cos(2x)
- sin(x)^2 cos(x)^2 cos(2x) = cos(2x)
cos(2x) [ 1 + sin(x)^2 cos(x)^2 ] = 0

1 + sin(x)^2 cos(x)^2 = 0
(sin(x) cos(x))^2 = -1
Решений нет

cos(2x) = 0
2x = п/2 + пк
x = (п/4)(2k + 1)