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Question
Evaluate the following:
`tan{2tan^-1 1/5-pi/4}`
Solution
`tan(2tan^-1 1/5-pi/4)=tan(2 tan^-1 1/5-tan^-1 1)`
`=tan[tan^-1{(2xx1/5)/(1-(1/5)^2)}-tan^-1 1]` `[because2tan^-1x=tan^-1{(2x)/(1-x^2)}]`
`=tan[tan^-1{(2/5)/(24/25)}-tan^-1 1]`
`=tan[tan^-1 5/12+tan^-1 1]`
`=tan[tan^-1((5/12-1)/(1+5/12))]` `[becausetan^-1x-tan^-1y=tan^-1((x+y)/(1+xy))]`
`=tan[tan^-1((-7/12)/(17/12))]`
`=tan[tan^-1 -7/17]`
`=-7/17`
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