[tex]\\ \sf\longmapsto \displaystyle{\lim_{x\to 0}}\dfrac{sinx-sin3x}{sins3x-sinx}[/tex]
[tex]\boxed{\sf \displaystyle\lim_{x\to 0}\dfrac{f(x)}{g(x)}=\dfrac{\lim_{x\to 0}f(x)}{\lim_{x\to 0}g(x)}}[/tex]
Now
[tex]\\ \sf\longmapsto \displaystyle{\dfrac{\lim_{x\to 0}sinx-\lim_{x\to 0}sin3x}{\lim_{x\to 0}sin3x-\lim_{x\to 0}sinx}}[/tex]
[tex]\boxed{\sf \displaystyle{\lim_{x\to 0}}f(x)=f(a)}[/tex]
[tex]\\ \sf\longmapsto \dfrac{sin0-sin3(0)}{sin3(0)-sin0}[/tex]
[tex]\\ \sf\longmapsto \dfrac{0-0}{0-0}[/tex]
[tex]\\ \sf\longmapsto \dfrac{0}{0}[/tex]
[tex]\\ \sf\longmapsto 0[/tex]
