jee-main 2015 Q79

jee-main · India · 10apr Addition & Double Angle Formulae Multi-Step Composite Problem Using Identities
If $\tan\left(\frac{\pi}{4} + \frac{\theta}{2}\right) = \tan^3\left(\frac{\pi}{4} + \frac{\alpha}{2}\right)$, then $\sin\theta = $:
(1) $\frac{\sin\alpha(3 + \sin^2\alpha)}{1 + 3\sin^2\alpha}$
(2) $\frac{\sin\alpha(3 - \sin^2\alpha)}{1 + 3\sin^2\alpha}$
(3) $\frac{\sin\alpha(3 + \cos^2\alpha)}{1 + 3\cos^2\alpha}$
(4) $\frac{\sin\alpha(3 - \cos^2\alpha)}{1 + 3\cos^2\alpha}$ 
If $\tan\left(\frac{\pi}{4} + \frac{\theta}{2}\right) = \tan^3\left(\frac{\pi}{4} + \frac{\alpha}{2}\right)$, then $\sin\theta = $:\\
(1) $\frac{\sin\alpha(3 + \sin^2\alpha)}{1 + 3\sin^2\alpha}$\\
(2) $\frac{\sin\alpha(3 - \sin^2\alpha)}{1 + 3\sin^2\alpha}$\\
(3) $\frac{\sin\alpha(3 + \cos^2\alpha)}{1 + 3\cos^2\alpha}$\\
(4) $\frac{\sin\alpha(3 - \cos^2\alpha)}{1 + 3\cos^2\alpha}$
Paper Questions
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