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

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

1 Answer
Jun 5, 2018

-(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