General value of $\theta $ satisfying the equation ${\tan ^2}\theta + \sec 2\theta - = 1$ is
$m\pi ,n\pi + \frac{\pi }{3}$
$m\pi ,n\pi \pm \frac{\pi }{3}$
$m\pi ,n\pi \pm \frac{\pi }{6}$
None of these
The number of solutions of $sin \,3x\, = cos\, 2x$ , in the interval $\left( {\frac{\pi }{2},\pi } \right)$ is
Number of solution$(s)$ of the equation $ln(1 + sin^2x) = 1 -ln(5 + x^2)$ is -
Let $X=\{x \in R: \cos (\sin x)=\sin (\cos x)\} .$ The number of elements in $X$ is
If $\sin 3\alpha = 4\sin \alpha \sin (x + \alpha )\sin (x - \alpha ),$ then $x = $
Let $A = \left\{ {\theta \,:\,\sin \,\left( \theta \right) = \tan \,\left( \theta \right)} \right\}$ and $B = \left\{ {\theta \,:\,\cos \,\left( \theta \right) = 1} \right\}$ be two sets. Then