If $\tan {\rm{\theta }} + \tan \left( {\frac{\pi }{3} + {\rm{\theta }}} \right) + \tan \left( { - \frac{\pi }{3} + {\rm{\theta }}} \right) = a\tan 3{\rm{\theta }},$ then $a$ is equal to

JEE MATHEMATICS MCQ: MULTIPLE AND SUBMULTIPLE ANGLES

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Application +4 | -1

\tan \mathrm{\theta } + \tan \left( {\frac{\pi }{3} + \mathrm{\theta }} \right) + \tan \left( { - \frac{\pi }{3} + \mathrm{\theta }} \right) = a\tan 3\mathrm{\theta },

then

a

is equal to

View answer and explanation

Correct option: C

Option C (3) is correct because by simplifying the given trigonometric expression, we find that

a = 3

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