If $cosx + secx =\, -2$, then for a $+ve$ integer $n$, $cos^n x + sec^n x$ is
always $2$
always $-2$
$-2$ if $n$ is odd and $2$ if $n$ is even
$-2$ if $n$ is even and $2$ if $n$ is odd
The number of solutions of the equation $\sin \theta+\cos \theta=\sin 2 \theta$ in the interval $[-\pi, \pi]$ is
If $3({\sec ^2}\theta + {\tan ^2}\theta ) = 5$, then the general value of $\theta $ is
The variable $x$ satisfying the equation $\left| {\sin \,x\,\cos \,x} \right| + \sqrt {2 + {{\tan }^2}\,x + {{\cot }^2}\,x} = \sqrt 3$ belongs to the interval
If $2\,cos\,\theta + sin\, \theta \, = 1$ $\left( {\theta \ne \frac{\pi }{2}} \right)$ , then $7\, cos\,\theta + 6\, sin\, \theta $ is equal to
The set of angles btween $0$ & $2\pi $ satisfying the equation $4\, cos^2 \, \theta - 2 \sqrt 2 \, cos \,\theta - 1 = 0$ is