1-2sin^2(2x)
isn't this a difference of two squares?
I assume it all is equal to zero...
(1-sqrt2*sin2x)(1+sqrt2*sin2x)=0
solve for 2x, then x.
To simplify the expression 1-2sin^2(2x), we can use the trigonometric identity: sin^2(x) + cos^2(x) = 1.
Let's start step by step:
Step 1: Apply the identity sin^2(x) + cos^2(x) = 1 to sin^2(2x):
1 - 2sin^2(2x) = 1 - 2(1 - cos^2(2x))
Step 2: Expand the squared term:
1 - 2(1 - cos^2(2x)) = 1 - 2 + 2cos^2(2x)
Step 3: Simplify the expression:
1 - 2 + 2cos^2(2x) = -1 + 2cos^2(2x)
So, the simplified form of 1 - 2sin^2(2x) is -1 + 2cos^2(2x).