Question

If $0^0<\theta <{90}^0$, then find the value of $\theta$ satisfying $2\sin \theta =\text{cosec}\theta$.

Answer 1

$2\sin \theta =co\sec \theta =\frac{1}{\sin \theta }$
$\Rightarrow {\sin }^2\theta =\frac{1}{2}$ or $\sin \theta =\frac{1}{\sqrt{2}}$
$(\because \theta is+ve)$
$\Rightarrow \sin \theta =\sin {45}^0$ or $\theta ={45}^0$