Question

the value of x for the minimum value of under root 3cos x+sin x is




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Answer 1

$The \: value \: of \: x \: for \: the \: minimum \\value \: of \: \sqrt{3} cos x + sin x \\= 2[ cosx cos \frac{\pi}{6} + sin x sin \frac{\pi }{6} ]\\= 2 cos \Big( x - \frac{\pi}{6} \Big)$

/* Minimum value of this at */

$x - \frac{\pi}{6} = \pi$

$\implies x = \pi + \frac{\pi}{6}$

$= \frac{ 6\pi + \pi}{6} \\= \frac{7\pi}{6}$

Therefore.,

$\red{ Value \:of \: x }\green { = \frac{7\pi}{6}}$

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