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Question
Solve the following equation for x:
`cos^-1((x^2-1)/(x^2+1))+1/2tan^-1((2x)/(1-x^2))=(2x)/3`
Solution
`cos^-1((x^2-1)/(x^2+1))+1/2tan^-1((2x)/(1-x^2))=(2x)/3`
`=>cos^-1((1-x^2)/(1+x^2))+1/2xx2tan^-1x=(2x)/3` `[becausetan^-1((2x)/(1-x^2))=2tan^-1x]`
`=>2tan^-1x+tan^-1x=(2x)/3` `[becausecot^-1((1-x^2)/(1+x^2))=2tan^-1x]`
`=>3tan^-1x=(2x)/3`
`=>tan^-1x=(2x)/9`
`=>x=tan((2x)/9)`
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