How do you evaluate $cos (pi/12)$ ?

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How do you evaluate $cos (pi/12)$ ?

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Answer 1 · 2016-04-06T23:43:23

$sqrt(2 + sqrt3)/2$

Explanation:

Apply the trig identity:
$cos (pi/6) = sqrt3/2 = 2cos^2 (pi/12) - 1$
$2cos^2 (pi/12) = 1 + sqrt3/2 =(2 + sqrt3)/2$
$cos^2 (pi/12) = (2 + sqrt3)/4$
$cos (pi/12) = sqrt(2 + sqrt3)/2$ --> $cos (pi/12)$ is positive.

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How do you evaluate $cos (pi/12)$ ?

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