find the exact value of : cos(2 arctan(4/3))

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19-11-2016
Mathematics

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find the exact value of : cos(2 arctan(4/3))

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nobillionaireNobley nobillionaireNobley · Answer 1 · 2016-11-22T13:28:52+01:00

nobillionaireNobley nobillionaireNobley

22-11-2016

cos(2 arctan(4/3)) = cos(2 arccos(3/5)) = cos^2(arccos(3/5)) - sin^2(arccos(3/5)) = cos^2(arccos(3/5)) - sin^2(arcsin(4/5)) = (3/5)^2 - (4/5)^2 = 9/25 - 16/25 = -7/25.

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