SOLUTION: Find the exact value of cos 75 degree

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Question 998441: Find the exact value of cos 75 degree
Answer by ikleyn(52817) About Me  (Show Source):
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Find the exact value of cos 75 degree
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First,  cos(75°) = sin(15°)     (the reduction formula).

Next,  sin(15°) = sin%28%2830%5E0%29%2F2%29 = sqrt%281-cos%2830%5E0%29%29%2F2%29 =       (formula of half-argument for sine) =
= sqrt%28%281-sqrt%283%29%2F2%29%2F2%29 = sqrt%28%282-sqrt%283%29%29%2F4%29 = sqrt%282-sqrt%283%29%29%2F2.

Answer.  cos(75°) = sqrt%282-sqrt%283%29%29%2F2.

See the lessons
    - Trigonometric functions of half argument  and
    - Trigonometric functions of half argument - Examples
in this site.