1. ## Evaluate the following

I have a problem, that i simply cannot get the right answer for. I have tried using the principles of Double-Angle Formulas and Sum and Difference Formulas but i am not sure if i am doing it correctly. I was hoping someone could walk me through this so that i know what to do and will be able to repeat this for other questions of this type

lim x-->a $\displaystyle [sin(a + 2x) - 2sin(a + x) + sin (a)]/x^2$

2. If $\displaystyle a=0,$ $\displaystyle f(x)=\frac{\sin(a+2x)+2\sin(a+x)+\sin a}{x^2}=\frac{\sin 2x+2\sin x}{x^2}$ and $\displaystyle \lim_{x\,\to\,0}f(x)$ does not exist.

If $\displaystyle a\ne0,$ then $\displaystyle f(x)$ is continuous at $\displaystyle a$ and so $\displaystyle \lim_{x\,\to\,a}f(x)$ is simply $\displaystyle f(a).$

3. I was able to figure this out as well however, my problem is simplifying f(a). Would you be able to help me out with this, Or is this the final answer?

4. just to update my progress, this is what i have so far

[4sin(a)(cos^2(a)-cos(a))]/(a^2)