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AP EAMCET · Maths · Trigonometric Equations

If \(\sin \alpha=\sin \beta\) and \(\cos \alpha=\cos \beta\), then \(\alpha-\beta=\) for some integer \(n\).

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

Answer & Solution

Correct Answer

(D) \(2 n \pi\)

Step-by-step Solution

Detailed explanation

It is given that, \(\sin \alpha=\sin \beta\) \(\Rightarrow 2 \sin \left(\frac{\alpha-\beta}{2}\right) \cos \left(\frac{\alpha+\beta}{2}\right)=0\) ...(i) and \(\cos \alpha=\cos \beta\)…