use an identity to write the expression as a single trigonometric function. \n±√(1 + cos 18x / 2)\n±√(1 +…
use an identity to write the expression as a single trigonometric function. \n±√(1 + cos 18x / 2)\n±√(1 + cos 18x / 2) = □ (simplify your answer.)
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:
$\cos9x$