Solution
= Solution
This is the defining difference quotient for the <derivative> of <sine> at $a$. Therefore
$$
\boxed{\lim_{x\to a}\frac{\sin x-\sin a}{x-a}=\cos a}.
$$
The result holds for every real constant $a$.
= Solution
This is the defining difference quotient for the <derivative> of <sine> at $a$. Therefore
$$
\boxed{\lim_{x\to a}\frac{\sin x-\sin a}{x-a}=\cos a}.
$$
The result holds for every real constant $a$.