Use a double or half angle formula to determine value of cos(13π/12)?

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Use a double or half angle formula to determine value of cos(13π/12)?

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Answer 1 · 2018-05-05T00:01:32

$- (2 + sqrt3)/2$

Explanation:

$cos ((13pi)/12) = cos (pi/12 + pi) = - cos (pi/12)$
Find $cos ((pi)/12)$ by using trig identity:
$2cos^2 a = 1 + cos 2a$ .
In this case:
$2cos^2 (pi/12) = 1 + cos (pi/6) = 1 + sqrt3/2 = (2 + sqrt3)/2$
$cos^2 (pi/12) = (2 + sqrt3)/4$
$cos (pi/12) = (2 + sqrt3)/2$ --> ( $cos (pi/12)$ is positive).
Finally,
$cos ((13pi)/12) = - cos (pi/12) = - (2 + sqrt3)/2$

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Use a double or half angle formula to determine value of cos(13π/12)?

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