Question

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)

Answer 1

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.