Question

How do you solve `Cos (2theta) = -sqrt3 / 2`?

Answer 1

`theta = 75^0, 105^0 , 255^0,285^0` where `theta<360`

Explanation:

we know `cos(180-30)=-sqrt3/2 or cos150=-sqrt3/2 :. 2 theta=150 or theta=75^0` Also `cos(180+30)=-sqrt3/2 or cos210=-sqrt3/2 :. 2 theta=105 or theta=105^0` Similarly `cos(540-30)=-sqrt3/2 or cos510=-sqrt3/2 :. 2 theta=255 or theta=255^0` Also `cos(540+30)=-sqrt3/2 or cos570=-sqrt3/2 :. 2 theta=570 or theta=285^0`[Ans]