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 (7\pi)/(18)\cos (5\pi)/(36)+\sin (7\pi)/(18)\sin (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=(7\pi)/(18),b=(5\pi)/(36)`

so, the given expression will be:

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