For the curve \( \sin x+\sin y=1 \) lying in the first quadrant there exists a constant \( \alph...

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For the curve \( \sin x+\sin y=1 \) lying in the first quadrant there exists a constant \( \alpha \) for which
\[
\lim _{x \rightarrow 0} x^{\alpha} \frac{d^{2} y}{d x^{2}}=L \text { (not zero) }
\]
The value of \( L \) :
(a) \( \frac{1}{2} \)
(b) 1
(c) \( \frac{1}{2 \sqrt{2}} \)
(d) \( \frac{1}{2 \sqrt{3}} \)
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