Which of the following pairs of function/functions has same graph? `y=tan(cos^(-1)x); y=(sqrt(1-x^2))/x` `y=t a n(cot^(-1)x);y=1/x` `y="sin"(tan^(-1)x); y=x/(sqrt(1+x^2))` `y="cos"(tan^(-1)x); y=sin(cot^(-1)x)`

Explanation

(i) `y = tan(cos^-1x) and y = sqrt(1-x^2)/x`

`=>y = tan(tan^-1(sqrt(1-x^2)/x)) and y = sqrt(1-x^2)/x`

`=>y = sqrt(1-x^2)/x and y = sqrt(1-x^2)/x`

`:.` Domain and range of both functions are same, so there graphs will be same.



(ii) `y = tan(cot^-1x) and y = 1/x`

`=>y = tan(tan^-1(1/x)) and y = 1/x`

`=>y = 1/x and y = 1/x`

...