The set of all values of $\lambda$ for which the equation $\cos ^2 2 x-2 \sin ^4 x-2 \cos ^2 x=\lambda$
$[-2,-1]$
$\left[-2,-\frac{3}{2}\right]$
$\left[-1,-\frac{1}{2}\right]$
$\left[-\frac{3}{2},-1\right]$
The set of values of $‘a’$ for which the equation, $cos\, 2x + a\, sin\, x = 2a - 7$ possess a solution is :
Common roots of the equations $2{\sin ^2}x + {\sin ^2}2x = 2$ and $\sin 2x + \cos 2x = \tan x,$ are
The number of real solutions $x$ of the equation $\cos ^2(x \sin (2 x))+\frac{1}{1+x^2}=\cos ^2 x+\sec ^2 x$ is
Number of solutions of $8cosx$ = $x$ will be
The number of solutions to $\sin \left(\pi \sin ^2 \theta\right)+\sin \left(\pi \cos ^2 \theta\right)=2 \cos \left(\frac{\pi}{2} \cos \theta\right)$ satisfying $0 \leq \theta \leq 2 \pi$ is