The number of solutions of the equation $\sin 2 x-2 \cos x+4 \sin x=4$ in the interval $[0,5 \pi]$ is :

The number of solutions of the equation $\sin 2 x-2 \cos x+4 \sin x=4$ in the interval $[0,5 \pi]$ is :
  1. 3
  2. 5
  3. 4
  4. 6

Solution

$ \text { } \begin{aligned} & \sin 2 x-2 \cos x+4 \sin x=4 \\ & \Rightarrow 2 \sin x \cdot \cos x-2 \cos x+4 \sin x-4=0 \\ & \Rightarrow(\sin x-1)(\cos x-2)=0 \end{aligned} $ $ \begin{aligned} & \because \cos x-2 \neq 0, \therefore \sin x=1 \\ & \therefore \quad x=\frac{\pi}{2}, \frac{5 \pi}{2}, \frac{9 \pi}{2} \end{aligned} $

Asked in: JEE Main 2013 (23 Apr Online)

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