Find the exact value of cos7(pi)/12 using sum and/or difference identities.

Answer 1

sometimes it is easier to think in degrees, and then switch back

7π/12 = 105 degrees and 105 = 60+45
both angles that we know

cos 105
= cos(60+45)
= cos60cos45 - sin60sin45
= (1/2)(√2/2) - (√3/2)(√2/2)
= (√2 - √6)/4

so cos7π/12 = (√2-√6)/4

Answer 2

cos 7π/12