express the given quantity in terms of sin x and cos x

Question

evaluate cos π⁄12

Answer 1

By the co-function identity, cos(x) = sin(π/2-x), so cos(π/12) = sin(π/2-π/12) = sin(6π/12-π/12) = sin(5π/12).

To find the exact value of cos(π/12), we can use the fact that cos(π/6) = √3/2 and use the half-angle formula for cosine:

cos(π/12) = √[(1 + cos(π/6))/2] = √[(1 + √3/2)/2] = √[(2 + √3)/4] = √(2 + √3)/2

Therefore, the exact value of cos(π/12) is √(2 + √3)/2.

Hope this helped!