Find the value of `tan^(-1)(tan(3pi)/4)`

Explanation

`:' tan^(-1)(tan x) =x` if `xepsilon(-(pi)/2,(pi)/2)`
As `(3pi)/r!in(-(pi)/2,(pi)/2):.tan^(-1)("tan"(3pi)/4)!=(3pi)/4`
`:.(3pi)/4 epsilon((pi)/2,(3pi)/2)`
graph of `y=tan^(-1)(tan x)` is as:

`:'` from the graph we can see that if `(pi)/2ltxlt(3pi)/2`,
then `tan^(-1)(tanx)=x-pi`
`:.tan^(-1)("tan"(3pi)/4)=(3pi)/4-pi=-(pi)/4`