# Explain how to evaluate cospi/12.

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### 2 Answers

We know that cos (pi/6) = (sqrt 3)/2

cos (pi/6) = cos 2*(pi/12) = 2*[cos (pi/12)]^2 - 1

=> (sqrt 3)/2 = 2*[cos (pi/12)]^2 - 1

=> 2*[cos (pi/12)]^2 = 1 + (sqrt 3)/2

=> [cos (pi/12)]^2 = 1/2 + (sqrt 3)/4

=> cos (pi/12) = sqrt [ 1/2 + (sqrt 3)/4]

**The value of cos (pi/12) = sqrt [ 1/2 + (sqrt 3)/4]**

We'll evaluate cos pi/12 apllying the half angle identity, since pi/12 is the half of pi/6.

The half angle identity:

cos (a/2) =sqrt[(1+cos a)/2]

cos pi/12 = sqrt[(1+cos pi/6)/2]

cos pi/6 = sqrt3/2

cos pi/12 = sqrt[(1 + sqrt3/2)/2]

cos pi/12 = sqrt[(2 + sqrt3)/4]

**cos pi/12 = [sqrt(2 + sqrt3)]/2**