QJEEM13Ma87c6: JEE Main 2013 Mathematics - Class 11 JEEM13Ma87c6 Solution: The expression can be written as:

Question

Verified Solution • 2025–26 Session moderate

The expression

{{\tan {\rm A}} \over {1 - \cot {\rm A}}} + {{\cot {\rm A}} \over {1 - \tan {\rm A}}}

can be written as:

Accepted Answer

Given expression can be written as

{{\sin A} \over {\cos A}} \times {{sin\,A} \over {\sin A - \cos A}} + {{\cos A} \over {\sin A}} \times {{\cos A} \over {\cos A - sin\,A}}

(As

\tan A = {{\sin A} \over {\cos A}}

and

\cot A = {{\cos A} \over {\sin A}}

)

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

= {{{{\sin }^2}A + \sin A\cos A + {{\cos }^2}\,A} \over {\sin A\cos A}}

= 1 + \sec\, A{\mathop{\rm cosec}\nolimits} \,A

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