How do you evaluate $cos (\frac{π}{12})$ $cos(pi/12)$ using the half angle formula?

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How do you evaluate $cos (\frac{π}{12})$ $cos(pi/12)$ using the half angle formula?

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Answer 1 · 2016-05-24T04:47:48

$\frac{\sqrt{2 + \sqrt{3}}}{2}$ $sqrt(2 + sqrt3)/2$

Explanation:

Trig identity -->
$cos (\frac{π}{6}) = \frac{\sqrt{3}}{2} = 2 {cos}^{2} (\frac{π}{12}) - 1$ $cos (pi/6) = sqrt3/2 = 2cos^2 (pi/12) - 1$
$2 {cos}^{2} (\frac{π}{12}) = 1 + \frac{\sqrt{3}}{2} = \frac{2 + \sqrt{3}}{2}$ $2cos^2 (pi/12) = 1 + sqrt3/2 = (2 + sqrt3)/2$
${cos}^{2} (\frac{π}{12}) = \frac{2 + \sqrt{3}}{4}$ $cos^2 (pi/12) = (2 + sqrt3)/4$
$cos (\frac{π}{12}) = \pm \frac{\sqrt{2 + \sqrt{3}}}{2}$ $cos (pi/12) = +- sqrt(2 + sqrt3)/2$ .
Take the positive answer because cos (pi/12) is positive.

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How do you evaluate $cos (\frac{π}{12})$ $cos(pi/12)$ using the half angle formula?

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How do you evaluate $cos (\frac{π}{12})$ $cos(pi/12)$ using the half angle formula?