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Trigonometrical Equations
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The number of solutions of the equation $sin\, 2x - 2\,cos\,x+ 4\,sin\, x\, = 4$ in the interval $[0, 5\pi ]$ is
A
$3$
B
$5$
C
$4$
D
$6$
(JEE MAIN-2013)
Solution
$\sin \,2x\, – 2\,\cos \,x\, + \,4\,\sin \,x\, = 4$
$ \Rightarrow \,2\,\sin \,x.\,\cos \,x – 2\,\cos \,x\, + \,4\,\sin \,x – 4 = 0$
$ \Rightarrow \,(\sin \,x – 1)(\cos \,x – 2)\, = \,0$
$\because \,\cos \,x\, – \,2\, \ne \,0\,,$ $\therefore \,\sin \,x\, = 1$
$\therefore \,\,x\, = \frac{\pi }{2},\frac{{5\pi }}{2},\frac{{9\pi }}{2}$
Standard 11
Mathematics
