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AP EAMCET · PHYSICS · Mathematics in Physics

If \(\alpha, \beta\) and \(\gamma\) are the angles made by a vector with \(\mathrm{x}, \mathrm{y}\) and z axes respectively, then \(\sin ^2 \alpha+\sin ^2 \beta=\)

  1. A \(\sin ^2 \gamma\)
  2. B \(\cos ^2 \gamma\)
  3. C \(1+\cos ^2 \gamma\)
  4. D \(1+\sin ^2 \gamma\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(1+\cos ^2 \gamma\)

Step-by-step Solution

Detailed explanation

\( \cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1 \) \( (1 - \sin^2 \alpha) + (1 - \sin^2 \beta) + \cos^2 \gamma = 1 \) \( 2 - (\sin^2 \alpha + \sin^2 \beta) + \cos^2 \gamma = 1 \) \( \sin^2 \alpha + \sin^2 \beta = 1 + \cos^2 \gamma \)