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Question
Write the following in the simplest form:
`cot^-1 a/sqrt(x^2-a^2),| x | > a`
Solution
Let x = a sec θ
Now,
`cot^-1 a/sqrt(x^2-a^2)=cot^-1(a/sqrt(a^2sec^2theta-a^2))`
`=cot^-1 a/(asqrt(tan^2theta`
`=cot^-1(cottheta)`
= θ
`=sec^-1 x/a`
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