The number of solutions of the equation $sin 2 x + 2 sin x - cos x - 1 = 0$ in the range of $0 \leq x \leq 2 π$

3

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4

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2

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None of these

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Solution

The correct option is A $3$
Let $sin x = s, cos x = c$
$\Rightarrow 2 s c + 2 s - c - 1 = 0 \Rightarrow 2 s (c + 1) - 1 (c + 1) = 0 \Rightarrow (2 s - 1) (c + 1) = 0 \Rightarrow s = \frac{1}{2} or c = - 1 \Rightarrow x = \frac{π}{6}, \frac{5 π}{6}, π$

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