Question

How do you find the exact values of cos 105 using the half angle formula?

Answer 1

Find cos 105

Ans: (2 - sqrt3)/2

Explanation:

cos 105 = cos (15 + 90) = - sin 15

`cos 30 = sqrt3/2 = 1 - 2sin^2 (15)`
`2sin^2 15 = (2 - sqrt3)/2`
`sin^2 15 = (2 - sqrt3)/4 --> sin 15 = +- (2 - sqrt3)/2`

Since the arc 15 is in Quadrant I, therefor, only the positive answer is accepted.

`cos 105 = - sin 15 = - (2 - sqrt3)/2`