Question

How do you use the angle sum identity to find the exact value of `cos255`?

Answer 1

Use the trig identity;
`2cos^2 a = 1 + cos 2a`
If a = 255 --> 2a = 510 -->
cos 2a = cos 510 = cos (150 + 360) = cos 150 =`- sqrt3/2`
`2cos^2 (255) = 1 + cos (150) = 1 - sqrt3/2 = (2 - sqrt3)/2`
`cos^2 (255) = (2 - sqrt3)/4`
`cos (255) = +- sqrt(2 - sqrt3)/2`