(a)OR(b)

Prove that : $\displaystyle \sqrt{\frac{1+\sin \mathrm{A}}{1-\sin \mathrm{A}}}=\sec \mathrm{A}+\tan \mathrm{A}$

\[\begin{aligned} \text { L.H.S. } & =\sqrt{\frac{1+\sin \mathrm{A}}{1-\sin \mathrm{A}} \times \frac{1+\sin \mathrm{A}}{1+\sin \mathrm{A}}} \\ & =\frac{1+\sin \mathrm{A}}{\sqrt{1-\sin ^{2} \mathrm{~A}}} \\ & =\frac{1+\sin \mathrm{A}}{\cos \mathrm{~A}} \\ & =\sec \mathrm{A}+\tan \mathrm{A}=\text { R.H.S. } \end{aligned} \]

\[\begin{aligned} & \frac{3 \times\left(\dfrac{\sqrt{3}}{2}\right)^{2}-6 \times(2)^{2}}{(\sqrt{3})^{2}} \\ = & -\frac{87}{12} \text { or }-\frac{29}{4} \end{aligned} \]