Nilai \( \displaystyle \lim_{x\to 0} \ \frac{\cos (x+a) - \cos (x-a)}{x} = \cdots \)
Pembahasan:
\begin{aligned} \lim_{x\to 0} \ \frac{\cos (x+a) - \cos (x-a)}{x} &= \lim_{x\to 0} \ \frac{-2 \sin \frac{1}{2} ((x+a)+(x-a)) \sin \frac{1}{2} ((x+a)-(x-a))}{x} \\[8pt] &= \lim_{x\to 0} \ \frac{-2 \sin x \ \sin a}{x} \\[8pt] &= -2 \sin a \ \cdot \ \lim_{x\to 0} \ \frac{\sin x}{x} \\[8pt] &= -2 \sin a \ \cdot \ 1 \\[8pt] &= -2 \sin a \end{aligned}