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How do you find cos 2x, given cot x = 3/5 and csc x < 0?

1 Answer

Vinícius Ferraz

Dec 5, 2015

# - 8/17#

Explanation:

#cos x / sin x = 3/5#

#(1 - sin^2 x) / sin^2 x = 9/25#

#9 sin^2 x = 25 - 25 sin^2 x#

#sin x = ± sqrt{ 25/34}#

#1/sin x < 0 Rightarrow sin x = - 5/ sqrt 34#

#cos 2x = (1 - sin^2 x) - sin^2 x = 1 - 2 * 25 / 34#

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