Question

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

Answer 1

Let $aϵR$ where the domain is R
$Ltf\left(x\right)=Ltginx\cos x=\sin a\cos a=f\left(a\right)$
$\underset{x\to a}{\overset{Lt}{\to }}f\left(x\right)=\sin x=\underset{x\to a}{\overset{Lt}{\to }}\left(\sin x\cos x\right)$
$=\sin a\cos a=f\left(a\right)$
hence thew function is continuous at $x=a,aϵR$