Conisder x = 4 `tan^(-1)((1)/(5)),y = tan^(-1)((1)/(70))and z = tan^(-1)((1)/(99))`.
What is x - y + z equal to ?

Options

A. `(pi)/(2)`
B. `(pi)/(3)`
C. `(pi)/(6)`
D. `(pi)/(4)`

Answer

D

Explanation

`x-y="tan"^(-1)(8281)/(8450) rArr tan^(-1)|(8281)/(8450)|+tan^(-1)((1)/(99))`
`=tan^(-1)|((8281)/(8450)+(1)/(99))/(1-(8281)/(8450)xx(1)/(99))|=tan^(-1)|((828269)/(836550))/((828269)/(836550))|=1`
`tan^(-1)=(1)=(pi)/(4)`
`therefore` Option (d) is correct.