AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\sin x+\sin y=\frac{\sqrt{3}+1}{2}\) and \(\cos x+\cos y=\) \(\frac{\sqrt{3}-1}{2}\), then \(\tan ^2\left(\frac{x-y}{2}\right)+\tan ^2\left(\frac{x+y}{2}\right)=\)
- A \(8+4 \sqrt{3}\)
- B \(6+4 \sqrt{3}\)
- C \(3+\sqrt{3}\)
- D \(12+6 \sqrt{3}\)
Answer & Solution
Correct Answer
(A) \(8+4 \sqrt{3}\)
Step-by-step Solution
Detailed explanation
It is given that \(\begin{array}{ll} \sin x+\sin y & =\frac{\sqrt{3}+1}{2} \\ 2 & 2 \sin \frac{x+y}{2} \cos \frac{x-y}{2}=\frac{\sqrt{3}^2+1}{2} \end{array}\) \(\Rightarrow \quad \sin \frac{x+y}{2} \cos \frac{x-y}{2}=\frac{\sqrt{3}+1}{4}\) ...(i) and…
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