Question

use an identity to write the expression as a single trigonometric function
±√(1 - cos18x)/2
±√(1 - cos18x)/2 = □ (simplify your answer.)

Explanation:

Step1: Recall the half - angle identity

The half - angle identity for sine is \(\sin\frac{\alpha}{2}=\pm\sqrt{\frac{1 - \cos\alpha}{2}}\).

Step2: Identify \(\alpha\)

In the given expression \(\pm\sqrt{\frac{1-\cos18x}{2}}\), we can identify \(\alpha = 18x\). Then \(\frac{\alpha}{2}=\frac{18x}{2}=9x\).

Answer:

\(\sin9x\)