 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2016/paper-2/19/c/ii/solution

This is the defining difference quotient for the derivative of sine at

a

. Therefore

x \to a lim \frac{sin x - sin a}{x - a} = cos a .

The result holds for every real constant

a

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