Question

Find the value of $\cos 2\theta ,$if $2\sin 2\theta =\sqrt{3}.$

Answer 1

Given data: $2\sin 2\theta =\sqrt{3}$

Finding the value of $2\theta$:

$$\begin{gathered} 2\sin 2\theta =\sqrt{3} \\ \Rightarrow \sin 2\theta =\frac{\sqrt{3}}{2} \\ \Rightarrow \sin 2\theta =\sin {60}^o \\ \Rightarrow 2\theta ={60}^o \\ \therefore 2\theta ={60}^o \end{gathered}$$

Finding the value of $\cos 2\theta$:

Substituting the values of $2\theta$, we get

$$\begin{gathered} \cos 2\theta =\cos {60}^o \\ \therefore \cos 2\theta =\frac{1}{2} \end{gathered}$$

Hence, $\cos 2\theta =\frac{1}{2}$.