cos^2x (Power to Double Angle)
1/2(1+cos2x)
The double angle formula for cosine states that:
cos(2x) = cos²(x) – sin²(x)
Now, if we rearrange this equation, we can solve for cos²(x) in terms of cos(2x) and sin²(x):
cos²(x) = cos²(2x)/2 + sin²(x)/2
We can replace sin²(x) with 1 – cos²(x), since sin²(x) + cos²(x) = 1:
cos²(x) = cos²(2x)/2 + (1-cos²(x))/2
Simplifying this equation, we get:
cos²(x) = (1/2)*(cos²(2x) + 1)
Therefore, the formula for cos²(x) in terms of double angle is:
cos²(x) = (1/2)*(cos²(2x) + 1)
This formula can be used to simplify trigonometric expressions involving cos²(x) in terms of the double angle formula.
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