MCQ
The expression$\frac{{\tan A}}{{1 - \cot A}} + \frac{{\cot A}}{{1 - tanA}}$  can be written as:
  • A
    $\sin A\cos A + 1$
  • $\sec A cosecA + 1$
  • C
    $\tan A + \cot A$
  • D
    $\sec A + cosec\;A$

Answer

Correct option: B.
$\sec A cosecA + 1$
b
$ = \frac{{\sin A}}{{\cos A}} \times \frac{{\sin A}}{{\sin A - \cos A}} + \frac{{\cos A}}{{\sin A}} \times \frac{{\cos A}}{{\cos A - \sin A}}$

$ = \frac{1}{{\sin A - \cos A}}\left\{ {\frac{{{{\sin }^3}A - {{\cos }^3}A}}{{\cos A\sin A}}} \right\}$

$ = \frac{{{{\sin }^2}A + \sin A\cos A + {{\cos }^2}A}}{{\sin A\cos A}}$ $ = 1 + \sec A\cos ecA$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free