Discuss the continuity of the following functions:
(a) `f(x) = sin x + cos x`
(b) `f(x) = sin x - cos x`
(c) `f(x) = sin x . cos x`

Explanation

It is known that if g and h are two continuous functions,g+h,g-h,andg,h are also continuous.

it has to proved first that `g(x)=sinx` and `h(x)=cosx` are continuous functions.

`Let g(x)=sinx`

It is evident that `g(x)=sinx` is defined for every real number.

Let c be a real number.Put `x=c+h`

if `x->c`, then `h->0`

`g(c)=sinc`

`lim_(h->0)g(x)=lim_(x->c)sinx`

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