Question 921737: If tanx= root 13/6, find exact value of cos2x... Please help, thorough steps and details to the answer. Thank you.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If tanx= root 13/6, find exact value of cos(2x).
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Note: cos(2x) = cos^2(x)-sin^2(x)
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Since tan = y/x, y = 13 and x = 6
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Then r = sqrt[13^2 + 6^2] = sqrt(205)
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So, cos(x) = x/r = 6/sqrt(205)
and sin(x) = y/r = 13/sqrt(205)
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Your Problem:
cos(2x) = [(6/sqrt(205))^2 - (13/sqrt(205))^2] = (36 - 169)/205 = 133/205
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Cheers,
Stan H.
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