Find the values of x for which the following pair of functions are identical.
(i) `f(x)=tan^(-1)x+cot^(-1)x " and " g(x)=sin^(-1)x +cos^(-1)x`
(ii) `f(x)=cos(cos^(-1)x) " and " g(x)=cos^(-1)(cosx)`

Explanation

(i) `f(x)=tan^(-1)x+cot^(-1)x ,x in R.`
` " and " g(x)=sin^(-1)x +cos^(-1)x=(pi)/(2) " for " x in [-1,1]`
Hence functions are identical if ` x in [-1,1].`
(ii) `f(x)=cos(cos^(-1)x)` is defined if `cos^(-1)x` is defined for which ` x in [-1,1].`
` g(x)=cos^(-1)(cosx)` is defined if `cosx in [-1,1],` which is true `AA x in R.` So, domain is R.
Thus, common domain of two functions is `[-1,1].`
` :. f(x) =x " and " g(x) =x " for " [-1,1].`