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Question

Question: \[\frac{1}{\tan 3A - \tan A} - \frac{1}{\cot 3A - \cot A} =\]...

1tan3AtanA1cot3AcotA=\frac{1}{\tan 3A - \tan A} - \frac{1}{\cot 3A - \cot A} =

A

tanA\tan A

B

tan2A\tan 2A

C

cotA\cot A

D

cot2A\cot 2A

Answer

cot2A\cot 2A

Explanation

Solution

1tan3AtanA1cot3AcotA\frac{1}{\tan 3A - \tan A} - \frac{1}{\cot 3A - \cot A}

=1tan3AtanA+tanAtan3Atan3AtanA=1tan2A=cot2A\frac{1}{\tan 3A - \tan A} + \frac{\tan A\tan 3A}{\tan 3A - \tan A} = \frac{1}{\tan 2A} = \cot 2A.