Question

Discuss the continuity of the following functions :
$f\left(x\right)=\sin x-\cos x$

Answer 1

Here the domain is R . 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 at $x=a,aϵR$