The set of values of $‘a’$ for which the equation, $cos\, 2x + a\, sin\, x = 2a - 7$ possess a solution is :
The set of values of $‘a’$ for which the equation, $cos\, 2x + a\, sin\, x = 2a - 7$ possess a solution is :
- A
$(-\infty , 2)$
- B
$[2, 6]$
- C
$(6, \infty )$
- D
$(-\infty, \infty )$
Similar Questions
The number of solutions of the pair of equations $ 2 \sin ^2 \theta-\cos 2 \theta=0 $, $ 2 \cos ^2 \theta-3 \sin \theta=0$ in the interval $[0,2 \pi]$ is
The number of solutions of the pair of equations $ 2 \sin ^2 \theta-\cos 2 \theta=0 $, $ 2 \cos ^2 \theta-3 \sin \theta=0$ in the interval $[0,2 \pi]$ is
- [IIT 2007]
If $\operatorname{cosec}^2(\alpha+\beta)-\sin ^2(\beta-\alpha)+\sin ^2(2 \alpha-\beta)=\cos ^2(\alpha-\beta)$ where $\alpha, \beta \in\left(0, \frac{\pi}{2}\right)$, then $\sin (\alpha-\beta)$ is equal to
If $\operatorname{cosec}^2(\alpha+\beta)-\sin ^2(\beta-\alpha)+\sin ^2(2 \alpha-\beta)=\cos ^2(\alpha-\beta)$ where $\alpha, \beta \in\left(0, \frac{\pi}{2}\right)$, then $\sin (\alpha-\beta)$ is equal to
- [KVPY 2009]
The general solution of $\sin x - \cos x = \sqrt 2 $, for any integer $n$ is
The general solution of $\sin x - \cos x = \sqrt 2 $, for any integer $n$ is
If $\sqrt 3 \cos \,\theta + \sin \theta = \sqrt 2 ,$ then the most general value of $\theta $ is
If $\sqrt 3 \cos \,\theta + \sin \theta = \sqrt 2 ,$ then the most general value of $\theta $ is
$2{\sin ^2}x + {\sin ^2}2x = 2,\, - \pi < x < \pi ,$ then $x = $
$2{\sin ^2}x + {\sin ^2}2x = 2,\, - \pi < x < \pi ,$ then $x = $