Question

State whether the following statement is true or false:

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

• A. True
• B. False

Answer 1

The correct option is A True

Given

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

$⟹\frac{\tan A+\tan B}{\frac{1}{\tan A}+\frac{1}{\tan B}}$

$⟹\frac{\tan A+\tan B}{\frac{\tan A+\tan B}{\tan A\tan B}}$

$⟹\frac{1}{\frac{1}{\tan A\tan B}}$

$⟹\tan A\tan B$