Question

$\cos 2x+a\sin x=2a-7$ possesses a solution for

• A. all value of a
• B. a > 6
• C. a < 2
• D. 2 $\le$ a $\le$ 6

Answer 1

The correct option is D 2 $\le$ a $\le$ 6

$\cos 2x+a\sin x=2a-7$

$1-2{\sin }^{2}x+a\sin x=2a-7$

$\Rightarrow \sin x=\frac{1\pm \sqrt{a^2-8(2a-8)}}{4}=\frac{a\pm (a-8)}{4}$

$\Rightarrow \sin x=\frac{a-4}{2},2$(not possible)

Hence, $\sin x=\frac{a-4}{2}$

Since, $-1\le \sin x\le 1$

$-1\le \frac{a-4}{2}\le 1$

$\Rightarrow 2\le a\le 6$