Double Angle Identity for Cosine II (sin)
cos2x=1-2sin^2(x)
The double angle identity for cosine states that:
cos(2θ) = 1 – 2sin^2(θ)
To rewrite this identity using sin, we can start with the Pythagorean identity for sine and cosine:
sin^2(θ) + cos^2(θ) = 1
Solving for cos^2(θ), we get:
cos^2(θ) = 1 – sin^2(θ)
Now we can substitute this into the double angle identity for cosine:
cos(2θ) = 1 – 2sin^2(θ)
cos(2θ) = cos^2(θ) – sin^2(θ)
cos(2θ) = (1 – sin^2(θ)) – sin^2(θ)
cos(2θ) = 1 – 2sin^2(θ)
Therefore, the double angle identity for cosine can also be expressed using sine as:
cos(2θ) = 1 – 2sin^2(θ)
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