use an identity to simplify the expression. do not use a calculator. cos²(π/11) - sin²(π/11) cos²(π/11)…

Explanation:

Step1: Recall double - angle identity

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

Step2: Substitute $\alpha=\frac{\pi}{11}$

Let $\alpha = \frac{\pi}{11}$, then $\cos^{2}(\frac{\pi}{11})-\sin^{2}(\frac{\pi}{11})=\cos(2\times\frac{\pi}{11})=\cos(\frac{2\pi}{11})$.

Answer:

$\cos(\frac{2\pi}{11})$