The real roots of the equation $cos^7x\, +\, sin^4x\, =\, 1$ in the interval $(-\pi, \pi)$ are
$ \{- \frac{\pi }{2}\,,\,0 \}$
$\{ - \frac{\pi }{2}\,,\,0\,,\,\frac{\pi }{2} \}$
$\{ \frac{\pi }{2}\,,\,0 \}$
$\{ 0\,\,,\,\,\frac{\pi }{4}\,\,,\,\frac{\pi }{2} \}$
If $\alpha ,\beta ,\gamma $ be the angles made by a line with $x, y$ and $z$ axes respectively so that $2\left( {\frac{{{{\tan }^2}\,\alpha }}{{1 + {{\tan }^2}\,\alpha }} + \frac{{{{\tan }^2}\,\beta }}{{1 + {{\tan }^2}\,\beta }} + \frac{{{{\tan }^2}\,\gamma }}{{1 + {{\tan }^2}\,\gamma }}} \right) = 3\,{\sec ^2}\,\frac{\theta }{2},$ then $\theta =$
The number of points in $(-\infty, \infty)$, for which $x^2-x \sin x-\cos x=0$, is
Number of solutions of equation $secx = 1 + cosx + cos^2x + ........ \infty$ in $x \in [-50 \pi, 50 \pi]$ is -
If $0 \le x < 2\pi $ , then the number of real values of $x,$ which satisfy the equation $\cos x + \cos 2x + \cos 3x + \cos 4x = 0$ is . . .
$\sin 6\theta + \sin 4\theta + \sin 2\theta = 0,$ then $\theta = $