Question

If the equation asinx + cos2x = 2a–7 possesses a solution then a $ϵ$

• A. (0, 4)
• B. (2, $\infty$)
• C. [2, 11]
• D. [2, 6]

Answer 1

The correct option is D [2, 6]

$2si{n}^{2}x-asinx+(2a-8)=0$
$\Rightarrow sinx=\frac{a\pm (a-8)}{4}\Rightarrow sinx=\frac{a-4}{2}$
$\therefore -1\le \frac{a-4}{2}\le 1\Rightarrow 1\Rightarrow aϵ[2,6]$