The value of definite integral \( \int_{-1}^{1}\left(\tan ^{-1}\left(\sin \left(\cos ^{-1} x\rig...

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The value of definite integral \( \int_{-1}^{1}\left(\tan ^{-1}\left(\sin \left(\cos ^{-1} x\right)\right)\right)+\cot ^{-1}\left(\cos \left(\sin ^{-1} x\right)\right) d x \) is equal to:
(a) 0
(b) -1
(c) 1
(d) \( \pi \)
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