Y = 1 - cos^2 x

what is the question?

y' = sin 2x

To simplify the expression Y = 1 - cos^2(x), we can use the trigonometric identity for the square of cosine:

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

Using this identity, we can rewrite the expression as:

Y = 1 - (1 - sin^2(x))

Simplifying further:

Y = 1 - 1 + sin^2(x)

Y = sin^2(x)

Therefore, the simplified expression for Y is sin^2(x).