The value of
`tan^(-1)1/3+tan^(-1)1/5+tan^(-1)1/7+tan^(-1)1/8` is ……..

Options

A. `(11pi)/5`
B. `pi/4`
C. `pi`
D. `(3pi)/4`

Answer

B

Explanation

We have ,
`tan^(-1).(1)/(3) + tan^(-1).(1)/(5) + tan^(-1) tan^(-1).(1)/(7) + tan ^(-1).(1)/(8)`
`rArr tan^(-1)(((1)/(3)+(1)/(5))/(1-(1)/(3) xx (1)/(5))) + tan^(-1).(((1)/(7)+(1)/(8))/(1-(1)/(7) xx (1)/(8)))`
`(because tan ^(-1) x + tan^(-1) y = tan^(-1)((x+y)/(1-xy)))`
`= tan^(-1) ((8)/(14)) + tan^(-1)((15)/(55)) = tan^(-1)((4)/(7)) + tan^(-1)((3)/(11))`
`= tan^(-1).(((4)/(7) +(3)/(11))/(1-(4)/(7) xx (3)/(11))) = tan^(-1)((44+21)/(77-21))`
`=tan^(-1)((65)/(65)) = tan^(-1) (1) = (pi)/(4)`