The general value of $\theta $ satisfying the equation $\tan \theta + \tan \left( {\frac{\pi }{2} - \theta } \right) = 2$, is
$n\pi - \frac{\pi }{4}$
$n\pi + \frac{\pi }{4}$
$2n\pi \pm \frac{\pi }{4}$
$n\pi + {( - 1)^n}\frac{\pi }{4}$
The sum of all $x \in[0, \pi]$ which satisfy the equation $\sin x+\frac{1}{2} \cos x=\sin ^2\left(x+\frac{\pi}{4}\right)$ is
No. of solution of equation $sin^{65}x\, -\, cos^{65}x =\, -1$ is, if $x \in (-\pi , \pi )$
If $\cos A\sin \left( {A - \frac{\pi }{6}} \right)$ is maximum, then the value of $A$ is equal to
If $\cos 2\theta = (\sqrt 2 + 1)\,\,\left( {\cos \theta - \frac{1}{{\sqrt 2 }}} \right)$, then the value of $\theta $ is
The equation $2{\cos ^2}\left( {\frac{x}{2}} \right)\,{\sin ^2}x\, = \,{x^2}\, + \,\frac{1}{{{x^2}}},\,0\,\, \leqslant \,\,x\,\, \leqslant \,\,\frac{\pi }{2}\,\,$ has