Question

The value of x for the minimum value of √3 cosx + sinx is
(A) :- 180 degree
(B) :- 270 degree
(C) :- 210 degree
(D) :- 0 degree​

Answer 1

Answer:

option C is right answer...

Answer 2

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

$Minimum\: value \: of \: this \: at$

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

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

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

$= \frac{7\pi}{6} \\= \frac{ 7 \times 180\degree }{6} \\= 7 \times 30 \\= 210 \degree$

Therefore.,

$Option \: \green { ( C ) } \: is \: correct.$

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