AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\alpha, \beta\) are the acute angles such that \(\frac{\sin \alpha}{\sin \beta}=\frac{6}{5}\) and \(\frac{\cos \alpha}{\cos \beta}=\frac{9}{5 \sqrt{5}}\) then \(\sin \alpha=\)
- A \(\frac{4}{5}\)
- B \(\frac{3}{5}\)
- C \(\frac{3}{4}\)
- D \(\frac{2}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{4}{5}\)
Step-by-step Solution
Detailed explanation
\(\sin^2 \beta + \cos^2 \beta = 1\) \(\left(\frac{5}{6} \sin \alpha\right)^2 + \left(\frac{5 \sqrt{5}}{9} \cos \alpha\right)^2 = 1\) \(\frac{25}{36} \sin^2 \alpha + \frac{125}{81} (1 - \sin^2 \alpha) = 1\) \(225 \sin^2 \alpha + 500 (1 - \sin^2 \alpha) = 324\)…
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