Question

The expression $\frac{1}{\tan 3A-\tan A}-\frac{1}{\cot 3A-\cot A}$ is equal to

• A. $\cot 2A$
• B. $\tan 2A$
• C. $\cot 3A$
• D. $\tan 3A$

Answer 1

The correct option is A $\cot 2A$

$\frac{1}{\tan 3A-\tan A}-\frac{1}{\cot 3A-\cot A}$

$=\frac{1}{\frac{1}{\cot 3A}-\frac{1}{\cot A}}-\frac{1}{\cot 3A-\cot A}$

$=\frac{\cot A\cot 3A}{\cot A-\cot 3A}-\frac{1}{\cot 3A-\cot A}$

$=\frac{1+\cot A\cot 3A}{\cot A-cot3A}$

$=\cot (3A-A)=\cot 2A$

Hence, option (a) is correct.