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WBJEE · Maths · Trigonometric Equations

If \(\sin 6 \theta+\sin 4 \theta+\sin 2 \theta=0\), then general
value of \(\theta\) is

  1. A \(\frac{n \pi}{4}, n \pi \pm \frac{\pi}{3}\)
  2. B \(\frac{n \pi}{4}, n \pi \pm \frac{\pi}{6}\)
  3. C \(\frac{n \pi}{4}, 2 n \pi \pm \frac{\pi}{3}\)
  4. D \(\frac{n \pi}{4}, 2 n \pi \pm \frac{\pi}{6}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{n \pi}{4}, n \pi \pm \frac{\pi}{3}\)

Step-by-step Solution

Detailed explanation

We have, \(\sin 6 \theta+\sin 4 \theta+\sin 2 \theta=0\) \(\Rightarrow \quad \sin 6 \theta+\sin 2 \theta+\sin 4 \theta=0\) \(\Rightarrow \quad 2 \sin 4 \theta \cdot \cos 2 \theta+\sin 4 \theta=0\) \(\Rightarrow \quad \sin 4 \theta(2 \cos 2 \theta+1)=0\)…