The general solution of the trigonometric equation $tan\, x + tan \,2x + tan\, 3x = tan \,x · tan\, 2x · tan \,3x$ is
$x = n\pi$
$n\pi ± \frac{\pi }{3}$
$x = 2n\pi$
$x = \frac{{n\pi }}{3}$ where $n \in I$
The number of roots of the equation $\cos ^7 \theta-\sin ^4 \theta=1$ that lie in the interval $[0,2 \pi]$ is
If both roots of quadratic equation ${x^2} + \left( {\sin \,\theta + \cos \,\theta } \right)x + \frac{3}{8} = 0$ are positive and distinct then complete set of values of $\theta $ in $\left[ {0,2\pi } \right]$ is
The general solution of the trigonometric equation $\tan \theta = \cot \alpha $ is
The solution of equation ${\cos ^2}\theta + \sin \theta + 1 = 0$ lies in the interval
The equation $\sin x + \cos x = 2$has