cos^2x (Power to Double Angle)
1/2(1+cos2x)
To derive the formula for cos^2x in terms of double angle:
We know that cos2x = cos(x + x) = cosxcosx – sinxsinx
Also, sin^2x + cos^2x = 1
Rearranging the above equation, we get cos^2x = 1 – sin^2x
Substituting sin^2x = 1 – cos^2x in the formula for cos2x, we get:
cos2x = cosxcosx – (1 – cos^2x)
Simplifying the equation, we get:
cos2x = 2cos^2x – 1
Rearranging the above equation, we get:
cos^2x = (1 + cos2x) / 2
Therefore, the formula for cos^2x in terms of double angle is:
cos^2x = (1 + cos2x) / 2.
This formula can be used to simplify trigonometric expressions involving cos^2x.
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