31. Use the identity x + y y sin x + sin y = 2 sin cos 2 to prove that sin(h/2) cos h sin(a + h) – sin a = h h/2 | sin x Then use the inequality < 1 for x # 0 to show that |sin(a + h) – sin a| < |h| for all a. Finally, prove rigorously that lim sin x = sin a.

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A: Hey since, there are multiple questions are posted, we will answer the first question.