Question

use an identity to write the expression as a single trigonometric function.
±√(1 + cos 18x / 2)
±√(1 + cos 18x / 2) = □ (simplify your answer.)

Explanation:

Step1: Recall the half - angle identity

The half - angle identity for cosine is $\cos\alpha=\pm\sqrt{\frac{1 + \cos2\alpha}{2}}$.
Let $2\alpha = 18x$, then $\alpha=9x$.

Step2: Substitute into the identity

Substituting $\alpha = 9x$ into the half - angle identity $\pm\sqrt{\frac{1+\cos2\alpha}{2}}$, we get $\pm\sqrt{\frac{1+\cos18x}{2}}=\cos9x$.

Answer:

$\cos9x$