Question

How do you use the angle difference identity to find the exact value of `cos75`?

Answer 1

`cos (75) = sqrt(2 - sqrt3)/2`

Explanation:

Use trig identity:
`cos 2a = 2cos^2 a - 1`
`cos 150 = 2cos^2 (75) - 1`
Trig table -->
`- sqrt3/2 = 2cos^2 (75) - 1`
`2cos^2 (75) = 1 - sqrt3/2 = (2 - sqrt3)/2`
`cos^2 (75) = (2 - sqrt3)/4`
`cos (75) = +- sqrt(2 - sqrt3)/2`
Since cos (75) is positive, take the positive answer.