Double Angle Identity for Cosine III (cos)
cos2x=2cos^2(x)-1
The double angle identity for cosine provides a way to express the cosine of a angle in terms of the cosine of half that angle. The third form of the double angle identity for cosine is given by:
cos(2θ) = 2cos²(θ) – 1
This identity can be derived from the angle addition formula for cosine:
cos(α + β) = cosαcosβ – sinαsinβ
Let β = α and simplify:
cos(2α) = cosαcosα – sinαsinα
cos(2α) = cos²(α) – sin²(α)
cos(2α) = 2cos²(α) – 1
Thus, we have obtained the double angle identity for cosine, which can be used to simplify complex trigonometric expressions involving cosines.
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