Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

Given$\frac{\mathrm{tanA}}{1-\mathrm{cotA}}+\frac{\mathrm{cotA}}{1-\mathrm{tanA}}$

$=\frac{{\sin }^2\mathrm{A}}{\mathrm{cosA}\left(\mathrm{sinA}-\mathrm{cosA}\right)}+\frac{{\cos }^2\mathrm{A}}{\sin A\left(\mathrm{cosA}-\mathrm{sinA}\right)}$

$=\frac{{\sin }^3\mathrm{A}-{\cos }^3\mathrm{A}}{\sin \mathrm{A} \cos \mathrm{A}\left(\sin \mathrm{A}-\cos \mathrm{A}\right)}$

$=\frac{{\sin }^2\mathrm{A}+{\cos }^2\mathrm{A}+\sin \mathrm{A} \cos \mathrm{A}}{\sin \mathrm{A} \cos \mathrm{A}}$

$=\mathrm{secAcosecA}+1$