Q. The number of values of a in [$0, 2\,\pi$] for which 2 $sin^3$ $\alpha-7$ $sin^2$ $\alpha + 7$ sin $\alpha = 2$, is :
Solution:
$2\,\sin^{3}\alpha-2=7\,\sin^{2}\alpha-7\sin\,\alpha$
$2\,\left(\sin\alpha-1\right)\,\left(\sin^{2}\alpha+1+\,\sin\alpha\right)=7\,\sin\alpha\,\left(\sin\alpha-1\right)$
$\Rightarrow \sin\,\alpha=1$ or
$2\,sin^{2}\alpha+2+2\,\sin\alpha=7\,\sin\alpha\,\left(\sin\alpha-t\right)\,\left(\sin\alpha-2\right)$
$\Rightarrow \sin\,\alpha=1$ or $\sin\alpha=\frac{1}{2}\,\because \sin\,\alpha\ne-2$
$\Rightarrow 3$ solutions
