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

(2+32)

Explanation:

cos(5π12)=cos(π12π)=cos(π12)
Find cos(π12) by using trig identity:'
cos2a=2cos2a1.
In this case
cos2a=cos(π6)=32
2cos2(π12)=1+32=2+32
cos2(π12)=2+34
cos(π12)=2+32 (because cos (pi/12) is positive)
Finally,
cos(5π12)=cos(π12)=2+32