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MHT CET · Maths · Trigonometric Equations

If \(1-\cos \theta=\sin \theta \cdot \sin \frac{\theta}{2}\), then the value of \(\theta\) is

  1. A \(2 \mathrm{n} \pi, 4 \mathrm{n} \pi, \mathrm{n} \in \mathbb{Z}\)
  2. B \(\frac{n \pi}{2}, \frac{n \pi}{3}, n \in \mathbb{Z}\)
  3. C \((2 n+1) \frac{\pi}{2}, n \in \mathbb{Z}\)
  4. D \((2 n-1) \frac{\pi}{4}, n \in \mathbb{Z}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(2 \mathrm{n} \pi, 4 \mathrm{n} \pi, \mathrm{n} \in \mathbb{Z}\)

Step-by-step Solution

Detailed explanation

\(2\sin^2 \frac{\theta}{2} = 2\sin \frac{\theta}{2} \cos \frac{\theta}{2} \cdot \sin \frac{\theta}{2}\) \(2\sin^2 \frac{\theta}{2} = 2\sin^2 \frac{\theta}{2} \cos \frac{\theta}{2}\)