Question

Rewrite the function using the power-reducing formulas.
f(x) = cos2 x

Answer 1

f(x) = cos 2x = 2 cos^2 x - 1

Explanation:

Here, we want to rewrite the given function using the power reducing formula

f(x) = cos 2x

Recall;

cos 2x = cos(x + x)

= cos x • cos x - sin x• sin x

= cos^2 x - sin^2 x

But Sin^2 x = 1 - cos^2x

Thus;

Cos^2x - sin^2 x = cos^2 x - (1 - cos^2 x)

= cos^2 x + cos^2 x - 1 = 2 cos^2 x - 1