If$\ \alpha,\beta,\gamma,\delta$ are four solutions of the equation $ an{\left( heta + \frac{\pi}{4} ight) = 3 an{3 heta,}}$ then $ an{\alpha an{\beta an{\gamma an{\delta\ }}}}$equals

Question

If$\ \alpha,\beta,\gamma,\delta$ are four solutions of the equation $	an{\left( 	heta + \frac{\pi}{4} ight) = 3	an{3	heta,}}$ then $	an{\alpha	an{\beta	an{\gamma	an{\delta\ }}}}$equals

Dr. Abubacker · Accepted Answer

(c)
$\frac{1 + 	an	heta}{1 - 	an	heta} = 3\left( \frac{3	an{	heta - 	an^{3}	heta}}{1 - 3	an^{2}	heta} ight)$
On simplification, we get
$3	an^{4}{	heta - 6	an^{2}{	heta + 8	an{	heta - 1 = 0}}}$
$	herefore\$Product of roots $= 	an{\alpha \bullet 	an{\beta \bullet 	an{\gamma \bullet 	an{\delta = - \frac{1}{3}}}}}$

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

Explanation

Reviewed by Dr. Abubacker

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