Question

Discuss the continuity of the following functions :
$f\left(x\right)=\sin x+\cos x$
here the domain is R

Answer 1

Let $aϵR$$\underset{x\to a}{\overset{Lt}{\to }}f\left(x\right)=\sin x=\underset{x\to a}{\overset{Lt}{\to }}(\sin x+\cos x)$
$=\sin a+\cos a$
$=f\left(a\right)=RHL=LHL$
$\therefore$ function is continuous everywhere .