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Show that f(x)=x-sinx is increasing for ...

Show that `f(x)=x-sinx` is increasing for all `x` in `R`

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`f(x)=x-sin x `
` f^{prime}(x)=1-cos x`
For` f(x)` to be increasing, we must have `f^{prime}(x)>0`
` Rightarrow 1-cos x>0`
` Rightarrow f^{prime}(x) geqslant 0 for all x in R[because `{Cos} x leqslant 1] ``
` ...
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