Question

Solve for $0^{\circ }<\theta <{90}^{\circ }$
1) $2\cos 3\theta =1$ 2)$2\sin 2\theta =\sqrt{3}$

Answer 1

$1)2{\cos }^2\theta =1\Rightarrow \cos 3\theta =\frac{1}{2}=\cos {60}^{\circ }\Rightarrow 3\theta ={60}^{\circ }\Rightarrow \theta =\frac{{60}^{\circ }}{3}={20}^{\circ }2)2\sin 2\theta =\sqrt{3}\Rightarrow \sin 2\theta =\frac{\sqrt{3}}{2}=\sin {60}^{\circ }\Rightarrow 2\theta ={60}^{\circ }\Rightarrow \theta ={30}^{\circ }$