MHT CET · Maths · Trigonometric Equations
If \(1-\cos \theta=\sin \theta \cdot \sin \frac{\theta}{2}\), then the value of \(\theta\) is
- A \(2 \mathrm{n} \pi, 4 \mathrm{n} \pi, \mathrm{n} \in \mathbb{Z}\)
- B \(\frac{n \pi}{2}, \frac{n \pi}{3}, n \in \mathbb{Z}\)
- C \((2 n+1) \frac{\pi}{2}, n \in \mathbb{Z}\)
- D \((2 n-1) \frac{\pi}{4}, n \in \mathbb{Z}\)
Answer & Solution
Correct Answer
(A) \(2 \mathrm{n} \pi, 4 \mathrm{n} \pi, \mathrm{n} \in \mathbb{Z}\)
Step-by-step Solution
Detailed explanation
\(2\sin^2 \frac{\theta}{2} = 2\sin \frac{\theta}{2} \cos \frac{\theta}{2} \cdot \sin \frac{\theta}{2}\) \(2\sin^2 \frac{\theta}{2} = 2\sin^2 \frac{\theta}{2} \cos \frac{\theta}{2}\)
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