If \( x=\tan ^{-1}\left(\frac{\sqrt{1+\sin t}+\sqrt{1-\sin t}}{\sqr...
If \( x=\tan ^{-1}\left(\frac{\sqrt{1+\sin t}+\sqrt{1-\sin t}}{\sqrt{1+\sin t}-\sqrt{1-\sin t}}\right) \)
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and \( y=\tan ^{-1}\left(\frac{\sqrt{1+t^{2}}-1}{t}\right) \), then \( \frac{d y}{d x}= \)
(A) \( \frac{1}{t^{2}-1} \)
(B) \( t^{2}+1 \)
(C) \( \frac{1}{t^{2}+1} \)
(D) \( t^{2}-1 \)
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