Question

Evaluate $\underset{x\to 0}{lim}\frac{\sin (a+x)+\sin (a-x)-2\sin a}{x\sin x}$

Answer 1

$\begin{array}{c}\underset{x\to o}{lim}\frac{{\left(a+x\right)}^2\sin \left(c+x\right)-a^2\mathrm{sinc}}{x}\\ =\underset{x\to o}{lim}\frac{{\left(a+x\right)}^2\cos \left(a+x\right)+2\left(a+x\right)\sin \left(a+x\right)}{1}\\ =a^2\cos a+2a\sin a\end{array}$