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Which of the following is/are correct?
(a)
\[
\begin{array}{l}
\cos \left(\cos \left(\cos ^{-1} 1\right)\right)\sin \left(\sin ^{-1}(\sin (\pi-1))\sin \left(\cos ^{-1}\right.\right. \\
(\cos (2 \pi-2))
\end{array}
\]
(b)
\[
\begin{array}{l}
\cos \left(\cos \left(\cos ^{-1} 1\right)\right)\sin \left(\cos ^{-1}(\cos 2 \pi-2)\right)\sin \left(\sin ^{-1}\right. \\
(\sin (\pi-1))\tan \left(\cot ^{-1}(\cot 1)\right)
\end{array}
\]
(c)
\[
\sum_{t=1}^{5000} \cos ^{-1}(\cos (2 t \pi-1))=\sum_{t=1}^{2500} \cot ^{-1}(\cot (t \pi+2))
\]
where \( t \in I \)
(d) \( \cot ^{-1} \cot \operatorname{cosec}^{-1} \operatorname{cosec} \sec ^{-1} \sec \tan \tan ^{-1} \cos \cos ^{-1} \sin ^{-1} \) \( \sin 4=4-\pi \)
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