I have to prove that $\sin x$ and $\sin 2x$ are linearly independent. So I need to show that $a\sin x + b\sin 2x = 0$ only if $a=b=0$. 

Though I am not entirely understanding why they are linearly independent. This equation is satisfied if $x=0$ regardless of the values of $a$ and $b$. How then can I show that they are linearly independent?