Find the sum of all the roots of the equation, \( \sin \sqrt{x}=-1 \), which are less than \( 10...

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Find the sum of all the roots of the equation, \( \sin \sqrt{x}=-1 \), which are less than \( 100 \pi^{2} \). Also Find the sum of the square roots of these roots. Now, can we conclude that all the roots \( \cos \sqrt{x}=0 \) are also the roots of \( \sin \sqrt{x}=-1 \) ? Justify your answer.
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