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Find $\cos\tan^{-1}\sin\cot^{-1}x$

$\begin{array}{1 1}(a)\;\sqrt{\large\frac{x^2+1}{x^2+2}}&(b)\;\sqrt{\large\frac{x^2-1}{x^2+2}}\\(c)\;\sqrt{\large\frac{x^2+2}{x^2+1}}&(d)\;\large\frac{x^2+1}{x^2+2}\end{array}$

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