Question

Prove:
$\frac{\cot A+\tan B}{\cot B+\tan A}=\cot A\tan B$

Answer 1

$LHS=\frac{\cot A+\tan B}{\cot B+\tan A}$

$=\frac{\frac{1}{\tan A}+\tan B}{\frac{1}{\tan B}+\tan A}=\frac{\frac{1+\tan A\tan B}{\tan A}}{\frac{1+\tan A\tan B}{\tan B}}=\frac{\tan B}{\tan A}=\cot A\tan B=RHS$