Mathematics - Application of Derivative Question with Solution | TestHub

$\because \mathrm{a}=\frac{4}{\sin \mathrm{x}}+\frac{1}{1-\sin \mathrm{x}}$, where a is least

$\Rightarrow \frac{\mathrm{da}}{\mathrm{dx}}=\left(\frac{-4}{{\sin }^2\mathrm{x}}+\frac{1}{(1-\sin \mathrm{x}{)}^2}\right)\cos \mathrm{x}=0$

$\because \cos \mathrm{x}\ne 0\Rightarrow \sin \mathrm{x}=2/3$

$\frac{d^{2}a}{d{x}^2}=45>0$ for $\sin x=2/3\Rightarrow \frac{4}{2/3}+\frac{1}{1-2/3}=6+3=9$