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Question
Write the function in the simplest form: `tan^(-1) 1/(sqrt(x^2 - 1)), |x| > 1`
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Solution
`tan^(-1) 1/(sqrt(x^2 - 1)`, |x| > 1
Put x = cosec θ ⇒ θ = cosec−1 x
`:. tan^(-1) 1/(sqrt(x^2 - 1)) = tan^(-1) 1/(sqrt(cosec^2 theta - 1))`
`= tan^(-1) (1/ cot theta) = tan^(-1) (tan theta)`
`= theta = cosec^(-1) x = pi/2 - sec^(-1) x`
`[cosec^(-1) x + sec^(-1) x = pi/2]`
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