Question

Prove the following statements.
$\frac{\cot A+\tan B}{\cot B+\tan A}=\cot A\tan B$.

Answer 1

LHS $=\frac{cotA+tanB}{cotB+tanA}$

$=\frac{\left(\frac{cosA}{sinA}\right)+\left(\frac{sinB}{cosB}\right)}{\left(\frac{cosB}{sinB}\right)+\left(\frac{sinA}{cosA}\right)}$

$=\left(\frac{cosAcosB+sinAsinB}{cosBcosA+sinAsinB}\right)\times \frac{sinBcosA}{sinAcosB}$

$=cotAtanB$