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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)

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lublana

Answer with Step-by-step explanation:

We are given that

LHS

[tex] cos 2x[/tex]

To prove that

[tex] cos 2x=cos^2x-sin^2 x[/tex]

[tex]cos(x+x)[/tex]

We know that

[tex]cos(x+y)=cos xcosy-sinx siny[/tex]

Using the formula

[tex]cos(x+x)=cosx\cdot cosx-sinx\cdot sinx[/tex]

[tex] cos2 x=cos^2 x-sin^2 x[/tex]

By using

[tex] cosx\cdot cosx=cos^2 x[/tex]

[tex]sinx\cdot sinx=sin^2 x[/tex]

LHS=RHS

Hence, proved.

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