The number of roots of the equation $\cos ^7 \theta-\sin ^4 \theta=1$ that lie in the interval $[0,2 \pi]$ is
$2$
$3$
$4$
$8$
If the equation $tan^4x -2sec^2x + [a]^2 = 0$ has atleast one solution, then the complete range of $'a'$ (where $a \in R$ ) is
(Note : $[k]$ denotes greatest integer less than or equal to $k$ )
If $\sin 3\alpha = 4\sin \alpha \sin (x + \alpha )\sin (x - \alpha ),$ then $x = $
Number of solution $(s)$ of equation $cosec\, \theta -cot \,\theta = 1$ in $[0,2 \pi]$ is-
Find the principal and general solutions of the equation $\sec x=2$
The general solution of $sin\, x + sin \,5x = sin\, 2x + sin \,4x$ is :