Question

cotA/1-cotA+ tanA/1-tanA=-1​

Answer 1

Given:

$\frac{\cot A}{1- \cot A} +\frac{\tan A}{1 - \tan A}$

To Find:

Show that, $\frac{\cot A}{1- \cot A} +\frac{\tan A}{1 - \tan A} = -1$

Solution:

$\frac{\cot A}{1- \cot A} +\frac{\tan A}{1 - \tan A}$

$=\frac{\frac{\cos A}{\sin A} }{1 - \frac{\cos A}{\sin A} } +\frac{\frac{\sin A}{\cos A} }{1- \frac{\sin A}{\cos A} }$

$=\frac{\cos A}{\sin A - \cos A} +\frac{\sin A}{\cos A - \sin A}$

$=\frac{\cos A}{\sin A - \cos A} -\frac{\sin A}{\sin A -\cos A}$

$=\frac{\cos A - \sin A}{\sin A - \cos A}$

$= - 1$

Hence proved.

Answer 2

Answer:

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