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Find the principal value of the following: cot [sin^(-1) {cos (tan^(-1) 1)}]

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Find the principal value of the following:

cot [sin-1 {cos (tan-1 1)}]

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Given, cot [sin-1 {cos (tan-1 1)}]

= cot [sin-1{cos \(\frac{\pi}{4}\)}]

= cot  [sin-1 (\(\frac{1}{\sqrt2}\))]

= cot \(\frac{\pi}{4}\) = 1

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