The equation 3 ^2 x + 10 x - 6 = 0 is satisfied, if - Vidyadip

MCQ

The equation $3{\sin ^2}x + 10\cos x - 6 = 0$ is satisfied, if

A
$x = n\pi \pm {\cos ^{ - 1}}(1/3)$
✓
$x = 2n\pi \pm {\cos ^{ - 1}}(1/3)$
C
$x = n\pi \pm {\cos ^{ - 1}}(1/6)$
D
$x = 2n\pi \pm {\cos ^{ - 1}}(1/6)$

✓

Answer

Correct option: B.

$x = 2n\pi \pm {\cos ^{ - 1}}(1/3)$

b
(b) $3{\sin ^2}x + 10\cos x - 6 = 0$

$3(1 - {\cos ^2}x) + 10\cos x - 6 = 0$

On solving, $(\cos x - 3)\,(3\cos x - 1) = 0$

Either $\cos x = 3$, (which is not possible) or

$\cos x =\frac{1}{3}$ $ \Rightarrow \,\,x = 2n\pi \pm {\cos ^{ - 1}}(1/3)$.

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