If $\tan 2\theta \tan \theta = 1$, then the general value of $\theta $ is
$\left( {n + \frac{1}{2}} \right)\frac{\pi }{3}$
$\left( {n + \frac{1}{2}} \right)\,\pi $
$\left( {2n \pm \frac{1}{2}} \right)\frac{\pi }{3}$
None of these
If $K = sin^6x + cos^6x$, then $K$ belongs to the interval
If $\alpha ,\,\beta ,\,\gamma $ and $\delta $ are the solutions of the equation $\tan \left( {\theta + \frac{\pi }{4}} \right) = 3\,\tan \,3\theta $ , no two of which have equal tangents, then the value of $tan\, \alpha + tan\, \beta + tan\, \gamma + tan\, \delta $ is
$\alpha=\sin 36^{\circ}$ is a root of which of the following equation
If $\tan (\pi \cos \theta ) = \cot (\pi \sin \theta ),$ then the value of $\cos \left( {\theta - \frac{\pi }{4}} \right) =$
The number of distinct solutions of the equation $\log _{\frac{1}{2}}|\sin x|=2-\log _{\frac{1}{2}}|\cos x|$ in the interval $[0,2 \pi],$ is