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

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Answer 1 · 2015-05-03T22:52:31

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.

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