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How do you find all solutions (in the range 0 < x < pi) of the equation #cos 2x = - sqrt3 / 2#?

1 Answer

May 3, 2015

Use the trig identity: #2sin^2 a = 1 - cos 2a.#

#2sin^2 x = 1 - cos 2 x = 1 + (sqr3)/2 #= 1.866

#sin^2 x = 0.933 -> sin x = 0.966 -> x = 75 deg and x = 105.#

Within interval (0, 180) there are 2 answers: 75 and 105 deg.

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