AP EAMCET · Maths · Trigonometric Equations
If \(\alpha, \beta\) are acute angles such that \(\sin \beta=2 \sin \alpha\) and \(3 \cos \beta=2 \cos \alpha\), then \(\sec (\alpha+\beta)=\)
- A \(4\)
- B \(\sqrt{15}\)
- C \(\sqrt{20}\)
- D \(5\)
Answer & Solution
Correct Answer
(A) \(4\)
Step-by-step Solution
Detailed explanation
Given: \(\sin \beta=2 \sin \alpha...(i)\) and \(3 \cos \beta=2 \cos \alpha \Rightarrow \cos \beta=\frac{2}{3} \cos \alpha...(ii)\) Now, \(\sin ^2 \alpha+\cos ^2 \beta=(2 \sin \alpha)^2+\left(\frac{2}{3} \cos \alpha\right)^2\)…
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