the exact value of cos 13π/8 is: a. √((2 - √2...

# Explanation: ## Step1: Rewrite the angle We know that $\frac{13\pi}{8}= \frac{16\pi - 3\pi}{8}=2\pi-\frac{3\pi}{8}$. Since $\cos(2\pi - \alpha)=\cos\alpha$, then $\cos\frac{13\pi}{8}=\cos\frac{3\pi}{8}$. ## Step2: Use the half - angle formula The half - angle formula for cosine is $\cos\frac{\alpha}{2}=\pm\sqrt{\frac{1 + \cos\alpha}{2}}$. Let $\alpha=\frac{3\pi}{4}$, then $\frac{\alpha}{2}=\frac{3\pi}{8}$. And $\cos\frac{3\pi}{4}=-\frac{\sqrt{2}}{2}$. So $\cos\frac{3\pi}{8}=\sqrt{\frac{1+\cos\frac{3\pi}{4}}{2}}=\sqrt{\frac{1-\frac{\sqrt{2}}{2}}{2}}=\sqrt{\frac{2 - \sqrt{2}}{4}}$. # Answer: A. $\sqrt{\frac{2-\sqrt{2}}{4}}$