How do you find the exact values of cos 165° using the half angle formula?

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How do you find the exact values of cos 165° using the half angle formula?

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Answer 1 · 2015-07-21T14:50:37

Find cos 165 deg

#Ans: - (sqrt(2 + sqrt3))/2#

Explanation:

Call cos 165 = cos t ->> cos 2t = cos 330 = cos (-30 + 360) = cos -30 = # cos 30 = (sqrt3)/2.#
Use trig identity: #cos 2t = 2cos^2 t - 1#
#2cos ^2 t = 1 + sqrt3/2 = (2 + sqrt3)/2#
#cos^2 t = (2 + sqrt3)/4#

#cos 165 = cos t = +- (sqrt(2 + sqrt3))/2#
Since 165 deg is in Quadrant II, take the negative number as answer.

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How do you find the exact values of cos 165° using the half angle formula?

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