Draw the graph of `y=tan (tan^(-1)x) or y = cot (cot^(-1) x)`

Explanation

`y=tan (tan^(-1)x)`
Clearly the domain of the function is R.
`Now -ooltxltoo`
`therefore" "-pi/2lttan^(-1)xltpi/2`
`therefore" "-oolttan(tan^(-1)x)leoo`
Also f(x)`=tan(tan^(-1)x)=x, " for "x in R`
`y=cot(cot^(-1)x)`
Clearly, the domain of the funcion is R.
`"Now "-ooltxltoo`
`therefore" "0ltcot^(-1)xltpi`
`therefore" "-ooltcot(cot^(-1)x)ltoo`
`"Also " f(x) = cot(cot^(-1)x)=x, " for " x in R`
Thus, the graph of both the functions it the straight line `y=x, x in R.`