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Prove: 4 tan^(-1) (1/5 )- tan^(-1)( 1/2...

Prove: ` 4 tan^(-1) (1/5 )- tan^(-1)( 1/239) = pi/4`

Text Solution

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`L.H.S.= 4tan^-1(1/5) - tan^-1(1/239)`
`=2(tan^-1(1/5)+tan^-1(1/5)) - tan^-1(1/239)`
`=2tan^-1((1/5+1/5)/(1-1/5**1/5))- tan^-1(1/239)`
`=2tan^-1(10/24) - tan^-1(1/239)`
`=2tan^-1(5/12) - tan^-1(1/239)`
`=tan^-1(5/12)+tan^-1(5/12) - tan^-1(1/239)`
`= tan^-1((5/12+5/12)/(1-5/12**5/12))- tan^-1(1/239)`
`= tan^-1((5/12+5/12)/(1-5/12**5/12))- tan^-1(1/239)`
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