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Question
Solve the following equation for x:
tan−1`((1-x)/(1+x))-1/2` tan−1x = 0, where x > 0
Solution
tan−1`((1-x)/(1+x))-1/2` tan−1(x) = 0
⇒ `tan^-1((1-x)/(1+x))=1/2tan^-1(x)`
⇒ `tan^-1 1-tan^-1x=1/2tan^-1(x)`
⇒ `tan^-1 1=3/2tan^-1(x)`
⇒ `pi/4=3/2tan^-1(x)`
⇒ `pi/6=tan^-1(x)`
⇒ `x=1/sqrt3`
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