If \( \sin x+\cos x=y^{2}-y+a \) is not satisfied by any real value of \( x \) for any \( y \), ....

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If \( \sin x+\cos x=y^{2}-y+a \) is not satisfied by any real
\( \mathrm{P} \)
value of \( x \) for any \( y \), then \( a \in \)
(1) \( \left(-\infty,-\sqrt{2}+\frac{1}{4}\right) \)
(2) \( \left(\sqrt{2}+\frac{1}{4}, \infty\right) \)
(3) \( \left(\sqrt{2}-\frac{1}{4}, \infty\right) \)
(4) \( \left(-\infty, \sqrt{2}-\frac{1}{4}\right) \)


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