The set of values of $‘a’$ for which the equation, $cos\, 2x + a\, sin\, x = 2a - 7$ possess a solution is :
$(-\infty , 2)$
$[2, 6]$
$(6, \infty )$
$(-\infty, \infty )$
Solve $\cos x=\frac{1}{2}$
Let $S=\left\{x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right): 9^{1-\tan ^2 x}+9^{\tan ^2 x}=10\right\}$ and $\beta=\sum_{x \in S} \tan ^2\left(\frac{x}{3}\right)$, then $\frac{1}{6}(\beta-14)^2$ is equal to
If $1\,\, + \,\,\sin \theta \,\, + \,\,{\sin ^2}\theta + \ldots .\,\,to\,\,\infty \,\, = \,\,4\, + 2\sqrt 3 ,\,\,0\,\, < \,\theta \,\,\pi ,\,\,\theta \,\, \ne \,\frac{\pi }{2}\,,$ then $\theta = $
The general solution of the trigonometric equation $tan\, x + tan \,2x + tan\, 3x = tan \,x · tan\, 2x · tan \,3x$ is
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 $k$ )