The equation $a S i n x + C o s 2 x = 2 a - 7$ possess
a solution only if

a>6

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2 \leq a \leq 6

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a > 2

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0 \leq a \leq 2

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Solution

The correct option is B $2 \leq a \leq 6$
putting $c o s 2 x = 1 - 2 s i n^{2} x$
we get
$2 s i n^{2} x - a s i n x + 2 a - 8 = 0$
this gives
$s i n x = \frac{a - 4}{2}, 2 (i g n o r e d)$
now $- 1 \leq \frac{a - 4}{2} \leq 1$
this gives the range of a

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