Find the value of the expression `sin[cot^(-1){cos(tan^-1 1)}]`

Explanation

`Let P=sin [cot ^{-1}{cos (tan ^{-1} 1)}]`
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=sin [cot ^{-1}(cos frac{pi}{4})] [because tan ^{-1} 1=frac{pi}{4}]`
`
=sin [cot ^{-1} frac{1}{sqrt{2}}] [because cos frac{pi}{4}=frac{1}{sqrt{2}}]`
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Let, cot ^{-1} frac{1}{sqrt{2}}=y Rightarrow cot y=frac{1}{sqrt{2}}`
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Rightarrow sin y=sqrt{frac{2}{3}} Rightarrow y=sin ^{-1} sqrt{frac{2}{3}}`
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therefore P=sin [sin ^{-1} sqrt{frac{2}{3}}]=sqrt{frac{2}{3}}`
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