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

Option: 1

3


Option: 2

5


Option: 3

4


Option: 4

6


Answers (1)

best_answer

\\\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

\\\because \cos x-2 \neq 0, \quad \therefore \sin x=1 \\ \therefore \quad x=\frac{\pi}{2}, \frac{5 \pi}{2}, \frac{9 \pi}{2}

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