Question

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

Answer 1

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.