Indicate the relation which can hold in their respective domain for infinite values of `xdot` `"tan"|tan^(-1)x|=|x|` (b) `"cot"|cot^(-1)x|=|x|` `tan^(-1)|tanx|=|x|` (d) `sin|sin^(-1)x|=|x|`

Explanation

`(a)tan(tan^-1(x))`
for `x<0 , tan(tan^-1(x))`implies
`=tan(-tan^-1(x))`
`=-tan(tan^-1(x))`
`=-x`
for `x>0 ,tan(tan^-1(x))`implies
`=tan(tan^-1(x))`
`=x`
hence,`"tan"|tan^(-1)x|=|x|`

`(b) cot(cot^-1(x))`
for `x<0 , cot(cot^-1(x))`implies
`=cot(-cot^-1(x))`
`=-cot(cot^-1(x))`
`=-x`
for `x>0 ,cot(cot^-1(x))`implies
`=cot(cot^-1(x))`
`=x`
hence,`"cot"|cot^(-1)x|=|x|`




`(c)tan^-1(tanx)`
for,`x in(pi/2,pi]uu[(-3pi)/2,2pi)`
`=tan^-1(tan(-x))`
`=tan^-1(-tan(x))`
`=-tan^-1(tan(x))`
`=-x`
for,`x in(0,pi/2]uu[(pi,3pi)/2)`
`tan^-1(tanx)`
`=x`


`(d)sin(sin^-1(x))`
for `x<0 , sin(sin^-1(x))`implies
`=sin(-sin^-1(x))`
`=-sin(sin^-1(x))`
`=-x`
for `x>0 ,sin(sin^-1(x))`implies
`=sin(sin^-1(x))`
`=x`
hence,`"sin"|sin^(-1)x|=|x|`