Question

How do you find the exact values of cos 165° using the half angle formula?

Answer 1

Find cos 165 deg

`Ans: - (sqrt(2 + sqrt3))/2`

Explanation:

Call cos 165 = cos t ->> cos 2t = cos 330 = cos (-30 + 360) = cos -30 = `cos 30 = (sqrt3)/2.`
Use trig identity: `cos 2t = 2cos^2 t - 1`
`2cos ^2 t = 1 + sqrt3/2 = (2 + sqrt3)/2`
`cos^2 t = (2 + sqrt3)/4`

`cos 165 = cos t = +- (sqrt(2 + sqrt3))/2`
Since 165 deg is in Quadrant II, take the negative number as answer.