Show that `f(x)=x+cosx-a` is an increasing function on `R` for all values of `a` .

Explanation

We have given

`f(x)=x+cosx-a`

Then

`f'(x)=1−sinx`

Since `−1<=sinx<=1` then we get,

`1−sinx>=0` for all` x in R`

So, `f′(x)>=0` for all `x in R`

Hence the function is increasing on `R` for all values of `a`.