Question

The number of values of $\theta$ which satisfy the equation $6si{n}^3\theta +25si{n}^2\theta -39sin\theta -70=0$ is

• A. 0
• B. 2
• C. 3
• D. infinite

Answer 1

The correct option is D infinite

$6{\sin }^3\theta +25{\sin }^2\theta -39\sin \theta -70=0\Rightarrow \left(\sin \theta -2\right)\left(\sin \theta +5\right)\left(6\sin \theta +7\right)=0$
$\Rightarrow \sin \theta \ne 2$ or $\sin \theta \ne -5$ or $\sin \theta =\frac{7}{6}$
$\Rightarrow \theta =2n\pi -\arcsin \frac{7}{6}$