Q44 / 125 · BITSAT 2014 · Mathematics

The solution of $(2 \cos x-1)(3+2 \cos x)=0$ in the interval $0 \leq x \leq 2 \pi$ is

  • A
    $\frac{\pi}{3}$
  • Correct answer
    B
    $\frac{\pi}{3}, \frac{5 \pi}{3}$
  • C
    $\frac{\pi}{3}, \frac{5 \pi}{3}, \cos ^{-1}\left(-\frac{3}{2}\right)$
  • D
    None of these

Solution

We have $(2 \cos x-1)(3+2 \cos x)=0$ If $2 \cos x-1=0,$ then $\cos x=\frac{1}{2}$ $\therefore x=\pi / 3,5 \pi / 3$ If $3+2 \cos x=0,$ the $\cos x=-3 / 2$ which is not possible.

Hence, the correct answer is option: 'B'.

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