How do you evaluate $cos (π/8)$ ?

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How do you evaluate $cos (π/8)$ ?

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Answer 1 · 2016-07-02T23:32:32

$(2 + sqrt2)/2$

Explanation:

Use the trig identity:
$2cos^2 a = 1 + cos 2a$
$2cos ^2 (pi/8) = 1 + cos (pi/4) = 1 + sqrt2/2 = (2 + sqrt2)/2$
$cos^2 (pi/8) = (2 + sqrt2)/4$
$cos (pi/8) = sqrt(2 + sqrt2)/2$ (since cos (pi/8) is positive)

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How do you evaluate $cos (π/8)$ ?

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How do you evaluate $cos (π/8)$ ?