To simplify this expression, we can use the trigonometric identity:
cos^2(x) = 1 - sin^2(x)
Substitute this identity into the expression:
5sin^4(2x) - 4sin^2(2x)(1-sin^2(2x)) - 4(1-sin^2(2x))^2 + 4(1-2sin^2(2x))^2 = 0
Expand the expression:
5sin^4(2x) - 4sin^2(2x) + 4sin^4(2x) - 16sin^2(2x) + 16 + 16sin^2(2x) - 8sin^4(2x) = 0
Combine like terms:
8sin^4(2x) - 4sin^2(2x) + 16 = 0
This is the simplified form of the given expression.
To simplify this expression, we can use the trigonometric identity:
cos^2(x) = 1 - sin^2(x)
Substitute this identity into the expression:
5sin^4(2x) - 4sin^2(2x)(1-sin^2(2x)) - 4(1-sin^2(2x))^2 + 4(1-2sin^2(2x))^2 = 0
Expand the expression:
5sin^4(2x) - 4sin^2(2x) + 4sin^4(2x) - 16sin^2(2x) + 16 + 16sin^2(2x) - 8sin^4(2x) = 0
Combine like terms:
8sin^4(2x) - 4sin^2(2x) + 16 = 0
This is the simplified form of the given expression.