cos 2x + a sin x = 2a – 7 has a solution if

a = 0

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Solution

The correct option is C
$c o s 2 x + α s i n x = 2 a - 7 \Rightarrow 1 - 2 s i n^{2} x + a s i n x = 2 a - 7 \Rightarrow 2 s i n^{2} x - a s i n x + 2 a - 8 = 0 \Rightarrow s i n x = \frac{a \pm \sqrt{a^{2} - 8 (2 a - 8)}}{4} = \frac{a \pm (a - 8)}{4} \Rightarrow s i n x = \frac{a - 4}{2} \Rightarrow - 1 \leq \frac{a - 4}{2} \leq 1 \Rightarrow - 2 \leq a - 4 \leq 2 \Rightarrow 2 \leq a \leq 6$

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