Question

Solve : $\cot \theta +cosec\theta =\sqrt{3}$ for values of $\theta$ between $0^{\circ }$ & ${360}^{\circ }$.

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${120}^{\circ }$
• D. ${180}^{\circ }$

Answer 1

The correct option is B ${60}^{\circ }$

$\cot \theta +cosec\theta =\sqrt{3}\Rightarrow \cot \frac{\theta }{2}=\sqrt{3}\Rightarrow \frac{\theta }{2}=n\pi +\frac{\pi }{6}\Rightarrow \theta =2n\pi +\frac{\pi }{3}$
For $\theta ϵ(0^o,{360}^o)$
$\Rightarrow \theta ={60}^o$