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Trigonometrical Equations
medium
यदि $(2\cos x - 1)(3 + 2\cos x) = 0,\,0 \le x \le 2\pi $, तो $x = $
A
$\frac{\pi }{3}$
B
$\frac{\pi }{3},\frac{{5\pi }}{3}$
C
$\frac{\pi }{2},\frac{{5\pi }}{3},{\cos ^{ - 1}}\left( { - \frac{3}{2}} \right)$
D
$\frac{{5\pi }}{3}$
Solution
$(2\cos x – 1)\,\,(3 + 2\cos x) = 0$
तब $\cos x = \frac{1}{2}{\rm{ }}$ चूँकि $\cos x \ne \frac{{ – 3}}{2}$
$ \Rightarrow $ $x = 2n\pi \pm \frac{\pi }{3};\,\,\left\{ \begin{array}{l}{\rm{ \,for \,\,}}n = 0,\,\,x = \frac{\pi }{3},\,\frac{{5\pi }}{3}\\{\rm{ \,for\,\, }}n = 1,\,\,x = \frac{{5\pi }}{3}\end{array} \right\}$
Standard 11
Mathematics
