Question

use an identity to write the expression as a single trigonometric function.
1 - 2 sin²2x

a. 1/2 sin 16x
b. 2 sin 4x
c. cos 8x
d. cos 4x

Explanation:

Step1: Recall double - angle identity

The double - angle identity for cosine is \(\cos2\alpha = 1 - 2\sin^{2}\alpha\).

Step2: Substitute \(\alpha = 2x\)

Let \(\alpha=2x\). Then \(1 - 2\sin^{2}(2x)=\cos(2\times2x)\).

Answer:

\(D.\ \cos4x\)