How to find an equivalent expression for the limit as x ->π of sin x - sin π / x - π?

Question

Would it be cos(x- π) or sin x - sin π or neither?

Answer 1

Recall that f'(c) = lim_x→c [(f(x) - f(c)) / (x - c)]

So the given limit is equivalent to f'(π), where f(x) = sinx.

Since f'(x) = cosx, the value of the limit is cosπ = -1