The limit would present itself in the form
[tex]\sin(0)\left[\cos\left(\dfrac{1}{0}\right)+\sin\left(\dfrac{1}{0}\right)\right][/tex]
Obviously, you can't evaluate the two expressions
[tex]\cos\left(\dfrac{1}{0}\right),\quad \sin\left(\dfrac{1}{0}\right)\right][/tex]
But since sine and cosine functions are always between -1 and 1, the sum of these will be a number between -2 and 2.
So, the limit presents itself in the form
[tex]\sin(0)\cdot M = 0[/tex]
Since you have the product of a quantity which tends to zero, sin(x), and a quantity which is bounded, cos(1/x^2)+sin(1/x^2).
