Question

How do you use the angle sum identity to find the exact value of cos 165?

Answer 1

`cos (165)= (sqrt3-1)/(2sqrt2)`

Ans: `- (sqrt3 + 1)/(2sqrt2)`

Explanation:

`cos (165)= cos(120+45)`

`cos(165) = cos 120·cos 45 - sin 120·sin 45 = (-1/2)·sqrt2/2 - sqrt3/2·sqrt2/2 = - sqrt2/2 (1/2 + sqrt3/2) =`

`cos (165)= -(sqrt3 + 1)/(2sqrt2)`

Check by calculator.
cos 165 = - 0.97 ; `- (sqrt3 + 1)/(2sqrt2) = - 2.732/2.828 = - 0.97.` OK