Show that f(x)=cos x is continuous for all values of x.

Explanation

Let x=a be any value .
At x=a
f(a)=cos a
R.H.L `underset(xrarr0)limf(x)=underset(hrarr0)limf(a+h)`
`=underset(hrarr0)lim cos (a+h)=cos a`
`L.H.L=underset(xrarra^-)(lim)f(x)=underset(hrarr0)limf(0-h)`
`=underset(hrarr0)limcos(a-h)=cosa`
`therefore` R.H.L =f (a) =L.H.L and a is arbitrary value of x.
`therefore` f(x) =cos x is continous for all values of x.
Hence proved