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damaskus [11]
3 years ago
15

Use the Addition Formula for Cosine to prove the Double-Angle Formula for Cosine. cos(2x) = cos2(x) − sin2(x) Rewrite 2x as x +

x, and use the Addition Formula for Cosine to simplify. cos(2x) = cos(x + x) = cos(x) cos(x)
Mathematics
1 answer:
andre [41]3 years ago
3 0

Answer with Step-by-step explanation:

We are given that

LHS

cos 2x

To prove that

cos 2x=cos^2x-sin^2 x

cos(x+x)

We know that

cos(x+y)=cos xcosy-sinx siny

Using the formula

cos(x+x)=cosx\cdot cosx-sinx\cdot sinx

cos2 x=cos^2 x-sin^2 x

By using

cosx\cdot cosx=cos^2 x

sinx\cdot sinx=sin^2 x

LHS=RHS

Hence, proved.

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