Question

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

• A. {$\pi$/3}
• B. {$\pi$/3, 5$\pi$/3}
• C. {$\pi$/3, 5$\pi$/3, cos${}^{-1}$(-3/2)}
• D. None of these.

Answer 1

Answer: (B)

{$\pi$/3, 5$\pi$/3}

We have 2cosx-1 = 0 or 3 + 2cosx = 0
But 3 + 2cosx = 0 gives cosx= -3/2 which is not possible. From 2 cos x -1 = 0, we get cos x = 1/2
whence x = $\pi$/3, 2$\pi$ - $\pi$/3, i.e., 5$\pi$ / 3 in the interval 0 $\le$ x $\le$ 2$\pi$. Thus the solution set in the given interval is {$\pi$/3, 5$\pi$/3}.