Question

If 2cos 3θ = 1, then θ = ?
(a) 10°
(b) 15°
(c) 20°
(d) 30°

Answer 1

(c) 20^o

$$\begin{gathered} 2\cos 3\theta =1 \\ \Rightarrow \cos 3\theta =\frac{1}{2} \\ \Rightarrow \cos 3\theta =\cos {60}^{\mathrm{o}}\left[\because \cos {60}^o=\frac{1}{2}\right] \\ \Rightarrow 3\theta ={60}^{\mathrm{o}} \\ \Rightarrow \theta =\frac{{60}^{\mathrm{o}}}{3}={20}^{\mathrm{o}} \end{gathered}$$