Write each of the following in the simplest form: `cot^(-1){a/(sqrt(x^2-a^2))},|x|> a`

Explanation

`cot^-1{a/sqrt(x^2 - a^2)}`

let `x= acosec theta`

`cot^-1 { a/sqrt(a^2 cosec^2 theta - a^2)}`

`cot^-1 { a/(a sqrt(cosec^2 theta -1))}`

`cot^-1 (tan theta)`

`cot^-1(cot(pi/2 - theta))`

`pi/2 - cosec^-1 (x/a) `

`= sec^-1 (x/a)`

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