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For the principal values, evaluate each ...

For the principal values, evaluate each of the following: `tan^(-1){2cos(2sin^(-1)(1/2))}`and

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

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`tan ^{-1} { [2 cos (2 sin ^{-1} frac{1}{2})] } `
`=tan ^{-1} [2 cos (2 times frac{pi}{6})] `
`=tan ^{-1} [2 cos frac{pi}{3}] quad ] `
`=tan ^{-1} [2 times frac{1}{2}] `
`=tan ^{-1}[1] `
`=frac{pi}{4} `
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