Question

What is the exact value of the following expression? cos (−5π/12)

Use the sum and difference identities to determine the exact value.

Answer 1

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

Explanation:

`cos ((-5pi)/12) = cos (pi/12 - pi) = - cos (pi/12)`
Find `cos (pi/12)` by using trig identity:'
`cos 2a = 2cos^2 a - 1`.
In this case
`cos 2a = cos (pi/6) = sqrt3/2`
`2cos^2 (pi/12) = 1 + sqrt3/2 = (2 + sqrt3)/2`
`cos^2 (pi/12) = (2 + sqrt3)/4`
`cos (pi/12) = sqrt(2 + sqrt3)/2` (because cos (pi/12) is positive)
Finally,
`cos ((-5pi)/12) = - cos (pi/12) = - sqrt(2 + sqrt3)/2`