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Question
Prove that
`tan^-1((1-x^2)/(2x))+cot^-1((1-x^2)/(2x))=pi/2`
Solution
`tan^-1((1-x^2)/(2x))+cot^-1((1-x^2)/(2x))=pi/2`
LHS = `tan^-1((1-x^2)/(2x))+cot^-1((1-x^2)/(2x))`
`=tan^-1((1-x^2)/(2x))+pi/2-tan^-1((1-x^2)/(2x))` `[becausetan^-1x+cot^-1x=pi/2]`
`=pi/2=` RHS
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