Question

find the value of cos 2 theta , 2 sin 2 theta =√3.

Answer 1

Here,
2sin2theta=√3
or,sin 2theta=√3/2
or,sin2theta=sin60°(since sin60°=√3/2)
or,2theta=60°
or,theta=30°....eq.1
Now,
cos2theta=cos2×30°=cos60°=1/2

Answer 2

The value of $\cos 2\theta$ = $\dfrac{1}{2}$

Step-by-step explanation:

We have,

2 $\sin 2\theta$ = $\sqrt{3}$

To find, the value of $\cos 2\theta$ = ?

∴ 2 $\sin 2\theta$ = $\sqrt{3}$

Dividing both sides by 2, we get

⇒ $\sin 2\theta$ = $\dfrac{\sqrt{3}}{2}$

⇒ $\sin 2\theta$ = $\sin 60$

⇒ 2θ = 60°

⇒ θ = 30°

∴ $\cos 2\theta$

= $\cos 2(30)$

= $\cos 60$

= $\dfrac{1}{2}$

∴ The value of $\cos 2\theta$ = $\dfrac{1}{2}$