The general solution of $\tan 3x = 1$ is
$n\pi + \frac{\pi }{4}$
$\frac{{n\pi }}{3} + \frac{\pi }{{12}}$
$n\pi $
$n\pi \pm \frac{\pi }{4}$
The expression $(1 + \tan x + {\tan ^2}x)$ $(1 - \cot x + {\cot ^2}x)$ has the positive values for $x$, given by
If $\tan (\pi \cos \theta ) = \cot (\pi \sin \theta ),$ then the value of $\cos \left( {\theta - \frac{\pi }{4}} \right) =$
Number of solution$(s)$ of the equation $\sin 2\theta + \cos 2\theta = - \frac{1}{2},\theta \in \left( {0,\frac{\pi }{2}} \right)$ is-
Let $S$ be the sum of all solutions (in radians) of the equation $\sin ^{4} \theta+\cos ^{4} \theta-\sin \theta \cos \theta=0$ in $[0,4 \pi]$ Then $\frac{8 \mathrm{~S}}{\pi}$ is equal to ...... .
Let $f(x)=\cos 5 x+A \cos 4 x+B \cos 3 x$ $+C \cos 2 x+D \cos x+E$, and
$T=f(0)-f\left(\frac{\pi}{5}\right)+f\left(\frac{2 \pi}{5}\right)-f\left(\frac{3 \pi}{5}\right)+\ldots+f\left(\frac{8 \pi}{5}\right)-f\left(\frac{9 \pi}{5}\right) \text {. }$Then, $T$