If $\;\alpha ,\,\,\beta ,\,\,\gamma ,\,\delta $ are four solutions of the equation $\tan \,\,\left( {{\rm{\theta }} + \frac{\pi }{4}} \right) = 3\,\,\tan \,3{\rm{\theta }}$, then $\tan \,\,\alpha \,\,\tan \,\,\beta \,\,\tan \,\,\gamma \,\,\tan \,\,\delta \;$ equals

JEE MATHEMATICS MCQ: MULTIPLE AND SUBMULTIPLE ANGLES

1 Easy

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Analyzing +4 | -1

\;\alpha ,\,\,\beta ,\,\,\gamma ,\,\delta

are four solutions of the equation

\tan \,\,\left( {\mathrm{\theta } + \frac{\pi }{4}} \right) = 3\,\,\tan \,3\mathrm{\theta }

, then

\tan \,\,\alpha \,\,\tan \,\,\beta \,\,\tan \,\,\gamma \,\,\tan \,\,\delta \;

equals

View answer and explanation

Correct option: C

- \frac{1}{3}

Option C (

\frac{{ - 1}}{3}

) is correct because the product of the roots of the quartic equation formed from the given trigonometric equation is equal to

\frac{{ - 1}}{3}