Question

use the sum and difference identities to rewrite the following expression as a trigonometric function of one angle. $cos(\frac{pi}{2})cos(\frac{3pi}{8})+sin(\frac{pi}{2})sin(\frac{3pi}{8})$ answer

Explanation:

Step1: Recall cosine - difference identity

The cosine - difference identity is $\cos(A - B)=\cos A\cos B+\sin A\sin B$.

Step2: Identify A and B

Let $A=\frac{\pi}{2}$ and $B = \frac{3\pi}{8}$.

Step3: Rewrite the expression

Using the identity $\cos(A - B)=\cos A\cos B+\sin A\sin B$, the given expression $\cos(\frac{\pi}{2})\cos(\frac{3\pi}{8})+\sin(\frac{\pi}{2})\sin(\frac{3\pi}{8})$ can be rewritten as $\cos(\frac{\pi}{2}-\frac{3\pi}{8})$.

Step4: Simplify the angle

Calculate $\frac{\pi}{2}-\frac{3\pi}{8}=\frac{4\pi - 3\pi}{8}=\frac{\pi}{8}$. So the expression is $\cos(\frac{\pi}{8})$.

Answer:

$\cos(\frac{\pi}{8})$