Question

Use a sum or difference formula to find the exact value of the following.771 517п5лCOS COS+ sinsin1836 18 36

Answer 1

Given:

$\cos \frac{7\pi}{18}\cos \frac{5\pi}{36}+\sin \frac{7\pi}{18}\sin \frac{5\pi}{36}$

We will use the following formula:

$\cos (a-b)=\cos a\cdot\cos b+\sin a\cdot\sin b$

By comparing the given expression with the previous formula:

$a=\frac{7\pi}{18},b=\frac{5\pi}{36}$

so, the given expression will be:

$\cos (\frac{7\pi}{18}-\frac{5\pi}{36})=\cos \frac{\pi}{4}=\frac{1}{\sqrt[]{2}}=\frac{\sqrt[]{2}}{2}$