AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\sin x+\sin y=\alpha, \cos x+\cos y=\beta\) then \(\operatorname{cosec}(x+y)=\)
- A \(\frac{\beta^2-\alpha^2}{\beta^2+\alpha^2}\)
- B \(\frac{2 \alpha \beta}{\beta^2-\alpha^2}\)
- C \(\frac{\alpha^2+\beta^2}{2 \alpha \beta}\)
- D \(\frac{2 \alpha \beta}{\beta^2+\alpha^2}\)
Answer & Solution
Correct Answer
(C) \(\frac{\alpha^2+\beta^2}{2 \alpha \beta}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Since } \sin x+\sin y=\alpha \\ & \Rightarrow 2 \sin \left(\frac{x+y}{2}\right) \cos \left(\frac{x-y}{2}\right)=\alpha \end{aligned}\) Since, \(\cos x+\cos y=\beta\)…
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