Solve for x:
1-2 cos^2(x)+cos^4(x)+2 sin^2(x)-cos(x) sin(x) sin(2 x) = 0
Reduce trigonometric functions:
-3/8 (-3+4 cos(2 x)-cos(4 x)) = 0
Multiply both sides by -8/3:
-3+4 cos(2 x)-cos(4 x) = 0
Transform -3+4 cos(2 x)-cos(4 x) into a polynomial with respect to cos(2 x) using cos(4 x) = 2 cos^2(2 x)-1:
-2+4 cos(2 x)-2 cos^2(2 x) = 0
Divide both sides by -2:
1-2 cos(2 x)+cos^2(2 x) = 0
Write the left hand side as a square:
(cos(2 x)-1)^2 = 0
Take the square root of both sides:
cos(2 x)-1 = 0
Add 1 to both sides:
cos(2 x) = 1
Take the inverse cosine of both sides:
2 x = 2 π n for n element Z
Divide both sides by 2:
Answer: |x = π n for n element Z
