If $\sqrt 2 \sec \theta + \tan \theta = 1,$ then the general value $\theta $ is
$n\pi + \frac{{3\pi }}{4}$
$2n\pi + \frac{\pi }{4}$
$2n\pi - \frac{\pi }{4}$
$2n\pi \pm \frac{\pi }{4}$
If $\cot \theta + \cot \left( {\frac{\pi }{4} + \theta } \right) = 2$, then the general value of $\theta $ is
The equation $3{\sin ^2}x + 10\cos x - 6 = 0$ is satisfied, if
The number of solutions of the equation $4 \sin ^2 x-4$ $\cos ^3 \mathrm{x}+9-4 \cos \mathrm{x}=0 ; \mathrm{x} \in[-2 \pi, 2 \pi]$ is :
The solution set of the equation $tan(\pi\, tanx) = cot(\pi\, cot\, x)$ is
The general solution of the trigonometric equation $tan\, x + tan \,2x + tan\, 3x = tan \,x · tan\, 2x · tan \,3x$ is