Question

Evaluate: $\frac{1-\tan A}{1-\cot A}=-\tan A$

Answer 1

L.H.S$=\frac{1-\tan A}{1-\cot A}$

$=\frac{1-\tan A}{1-\frac{1}{\tan A}}$

$=\frac{\tan A(1-\tan A)}{-(1-\tan A)}$

$=-\tan A$

$=$R.H.S

Hence proved.