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Question
Write the value of tan−1x + tan−1 `(1/x)`for x > 0.
Solution
`tan^-1x+tan^-1y=tan^-1((x+y)/(1-xy)), xy<1`
`thereforetan^-1x+tan^-1 1/x=tan^-1((x+1/x)/(1-x 1/x)),x>0`
`=tan^-1((x^2+1)/0)`
`=tan^-1 (oo)`
`=tan^-1(tan pi/2)`
`=pi/2`
`thereforetan^-1x+tan^-1 1/x=pi/2`
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