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AP EAMCET · Maths · Trigonometric Ratios & Identities

If \(\frac{\tan (\alpha+\beta-\gamma)}{\tan (\alpha-\beta+\gamma)}=\frac{\tan \gamma}{\tan \beta}\) and \(\beta \neq \gamma\), then the value of \(\sin 2 \alpha+\sin 2 \beta+\sin 2 \gamma\) is

  1. A 0
  2. B 1
  3. C 2
  4. D \(\frac{1}{2}\)
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(A) 0

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Given: \( \frac{\tan (\alpha+\beta-\gamma)}{\tan (\alpha-\beta+\gamma)}=\frac{\tan \gamma}{\tan \beta} \) Rearrange: \( \frac{\tan (\alpha+\beta-\gamma)}{\tan \gamma} = \frac{\tan (\alpha-\beta+\gamma)}{\tan \beta} \) Applying componendo and dividendo:…