The Expression TanA1-cot A+cot A1-TanA can be written as

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The Expression $\frac{TanA}{1 - \cot A} + \frac{\cot A}{1 - TanA}$ can be written as

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$SecA CosecA + 1$

$SecA + Cosec A$

$sinA Cos A + 1$

$TanA + Cot A$

answer is B.

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Detailed Solution

$\begin{array}{rcl} \frac{TanA}{1 - \cot A} + \frac{\cot A}{1 - TanA} \\ = & \frac{tanA sinA}{\sin A - \cos A} + \frac{\cot A cosA}{\cos A - \sin A} \\ = & \frac{\frac{\sin^{2} A}{\cos A} - \frac{\cos^{2} A}{\sin A}}{Sin A - Cos A} \\ = & \frac{\sin^{3} A - \cos^{3} A}{(sinA cosA) (sinA - cosA)} \\ = & \frac{(sinA - cosA) (\sin^{2} A + sinAcosA + \cos^{2} A)}{sinA cosA (sinA - cosA)} \\ = & \sec A cosecA + 1 \end{array}$