Jee Main 2024 27 01 2024 Shift 1 - Question14
Question 14
If $\cos 2 x-a \sin x=2 a-7$, then range of $a$ is
(1) $-2 \leq a \leq 0$
(2) $2 \leq a \leq 6$
(3) $a \geq 6$
(4) $6 \leq a \leq 8$
Show Answer
Answer: (2)
Solution:
$1-2 \sin ^{2} x-a \sin x=2 a-7$
$2 \sin ^{2} x+a \sin x+2 a-8=0$
$\sin x=\frac{-a \pm \sqrt{a^{2}-8(2 a-8)}}{4}$
$=\frac{-a \pm|a-8|}{4}$
$=-2$ or $\frac{8-2 a}{4}$
(-2) Not possible
$\therefore \sin x=\frac{8-2 a}{4}$
$-1 \leq \frac{8-2 a}{4} \leq 1$
$-4 \leq 8-2 a \leq 4$
$2 \leq a \leq 6$
BETA
