power reducing: sin^2(x)
(1-cos2x)/2
The power reducing formula for sin^2(x) is:
sin^2(x) = (1 – cos(2x))/2
This formula can be derived from the identity:
sin^2(x) + cos^2(x) = 1
By rearranging, we get:
sin^2(x) = 1 – cos^2(x)
Now, using the double angle formula for cosine:
cos(2x) = cos^2(x) – sin^2(x)
We can rearrange and substitute the previous identity to get:
cos(2x) = cos^2(x) – (1 – cos^2(x))
cos(2x) = 2cos^2(x) – 1
Substituting this into the power reducing formula for sin^2(x), we get:
sin^2(x) = (1 – cos(2x))/2
Therefore, we can use this formula to simplify expressions involving sin^2(x), such as integrating sin^2(x) with respect to x or solving trigonometric equations.
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