State whether `f(x)=tanx-x` is increasing or decreasing its domain.

Explanation

b`f(x)=tan x-x`
`
f^{prime}(x)=sec ^{2} x-1`
`
sec ^{2} x-1 geq 0`
`
sec ^{2} x geq 1`
`
because 1+tan ^{2} x=sec ^{2} x`
`
therefore 1+tan ^{2} x geq 1`
`
tan ^{2} x geq 0`
`
therefore tan ^{2} x geq 0 forall x in[0,2 pi] `
`
...