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MHT CET · Maths · Trigonometric Equations

The possible values of \(\theta \in(0, \pi)\) such that \(\sin \theta+\sin (4 \theta)+\sin (7 \theta)=0\) are

  1. A \(\frac{\pi}{4}, \frac{5 \pi}{12}, \frac{\pi}{2}, \frac{2 \pi}{3}, \frac{3 \pi}{4}, \frac{8 \pi}{9}\)
  2. B \(\frac{2 \pi}{9}, \frac{\pi}{4}, \frac{\pi}{2}, \frac{2 \pi}{3}, \frac{3 \pi}{4}, \frac{35 \pi}{36}\)
  3. C \(\frac{2 \pi}{9}, \frac{\pi}{4}, \frac{\pi}{2}, \frac{2 \pi}{3}, \frac{3 \pi}{4}, \frac{8 \pi}{10}\)
  4. D \(\frac{2 \pi}{9}, \frac{\pi}{4}, \frac{4 \pi}{9}, \frac{\pi}{2}, \frac{3 \pi}{4}, \frac{8 \pi}{9}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{2 \pi}{9}, \frac{\pi}{4}, \frac{4 \pi}{9}, \frac{\pi}{2}, \frac{3 \pi}{4}, \frac{8 \pi}{9}\)

Step-by-step Solution

Detailed explanation

\(\sin \theta+\sin (7 \theta)+\sin (4 \theta)=0\) \(2 \sin \left(\frac{\theta+7 \theta}{2}\right) \cos \left(\frac{\theta-7 \theta}{2}\right)+\sin (4 \theta)=0\)