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anonymous
 5 years ago
Trig Solve for 0< x< 2pi, exact values in radian .........cos (2 tan ^1(5/12))
anonymous
 5 years ago
Trig Solve for 0< x< 2pi, exact values in radian .........cos (2 tan ^1(5/12))

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0let y = tan^1(5/12) => tan(y) = 5/12 use sin^2y + cos^2y = 1 > 1 + tan^2y = [1/cos^2y] to find cos(y) in terms of tan(y) Than use double angle formula for cos(2x) to find cos(2y) in terms of cos(y).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\sin^2 y + \cos^2y = 1 \implies \tan^2y + 1 = \frac{1}{\cos^2y} \implies \cos^2 = \frac{1}{\tan^2y+1}\] We know tan(y) = 5/12 => tan^2 y = (5/12)^2 > cos^2 y = 144/169 > sin^2 y = 1 144/169 = 25/169 cos(2y) = cos^2(y)  sin^2 y = 144/169  25/169 = 119/169.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thank you very much, its greatly appreciated! :)
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