Question

The solution of \(\cos(2x)-1(3+2\cos x)=0\) in the interval \(0\le x\le2\pi\) is:

• A. \(\frac{\pi}{3}\)
• 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

Hint:

Reduce trigonometric equations to algebraic equations wherever possible.

Answer 1

The Correct Option is B

Step 1: \[ \cos2x=3+2\cos x \]
Step 2: Use identity \(\cos2x=2\cos^2x-1\).
Step 3: Solve quadratic in \(\cos x\) to get \[ \cos x=\frac{1}{2} \]