Question

$\cot \theta =\sin 2\theta (where\theta \ne n\pi ,nisaninteger)$ then $\theta =$

• A. ${45}^{\circ }and{60}^{\circ }$
• B. ${45}^{\circ }and{90}^{\circ }$
• C. $only{45}^{\circ }$
• D. $only{90}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }and{90}^{\circ }$

Given, $\cot \theta =\sin 2\theta$
or $\frac{\cos \theta }{\sin \theta }=2\sin \theta .\cos \theta$
or $\cos \theta (2{\sin }^2\theta -1)=0$
or $\cos \theta =0\text{or}\sin \theta =\pm \frac{1}{\sqrt{2}}$
Hence required solution is, $\theta ={45}^0,{90}^0$