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The number of values of $x$ in $[0,2\pi]$ satisfying the equation $3\cos 2x-10\cos x+7=0$ is?


1 Answer

Given :
$3\cos 2x-10\cos x+7=0$
$\Rightarrow\:3(2\cos^2x-1)-10\cos x+7=0$
$\Rightarrow\:6\cos^2x-10\cos x+4=0$
$\Rightarrow\:3\cos^2x-5\cos x+2=0$
$\Rightarrow\:(3\cos x-2)(\cos x-1)=0$
$\Rightarrow\:\cos x=1$ or $cos\:x=\large\frac{2}{3}$
$\Rightarrow\:x=0,2\pi$ or
or $x=2\pi-\cos^{-1}\large\frac{2}{3}$
Hence we have 4 solutions.
$(d)$ is the correct answer.
answered Nov 18, 2013 by sreemathi.v
edited Mar 25, 2014 by rvidyagovindarajan_1

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