Prove that: `tan^(-1)1/5+tan^(-1)1/7+tan^(-1)1/3+tan^(-1)1/8=pi/4`

Monjur Alahi

Prove that: `tan^(-1)1/5+tan^(-1)1/7+tan^(-1)1/3+tan^(-1)1/8=pi/4`


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Salim Ahmed Kawsar

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LHS=`tan^(-1)""(1)/(5)+tan^(-1)""(1)/(7)+ tan^(-1)""(1)/(3)+tan^(-1)""(1)/(8)`
`tan^(-1)""((1)/(5)+(1)/(7))/(1-(1)/(5)xx(1)/(7))+tan^(-1)""((1)/(3)+(1)/(8))/(1-(1)/(3)xx(1)/(8))`
`=tan^(-1)""((7+5)/(35))/((35-1)/(35))+tan^(-1)""(11)/(23)`
`=tan^(-1)""((6)/(17)+(11)/(23))/(1-(6)/(17)xx(11)/(23))=tan^(-1)""((138+187)/(391))/((391-66)/(391))`
`tan^(-1)""(352)/(325)=tan^(-1)1=(pi)/(4)`= RHS Hence Proved

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