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# For $0\;<\;x\;<\;\pi$, the values of x which satisfies $1+|cos\;x|+|cos\;x|^2+|cos\;x|^3+$....$\infty$ = $2^4$ are

$(a)\;\frac{\pi}{3}\;,\frac{3\pi}{4}\qquad(b)\;\frac{\pi}{3}\;,\frac{2\pi}{3}\qquad(c)\;\frac{\pi}{4}\;,\frac{3\pi}{4}\qquad(d)\;None\;of\;the\;above$

Answer : (b) $\frac{\pi}{3}\;,\frac{2\pi}{3}$
Explanation : $|cos\;x|\;<\;1$
$2^{2\;(\frac{1}{1-|cos\;x|})}=2^4$
$|cos\;x|=\frac{1}{2}$
$x=\frac{\pi}{3}\;,\frac{2\pi}{3}.$