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2 Prove that cos 3x = 4 cos3 x - 3 cos x . Find and prove a similar result for sin 3x in terms of sin x. (i) Let I(Â®) = Z Â® 0 Â¡ 7 sin x - 8 sin3 x Â¢ dx . Show that I(Â®) = -8 3 c3 + c + 5 3 , where c = cos Â®. Write down one value of c for which I(Â®) = 0. (ii) Useless Eustace believes that Z sinn x dx = sinn+1 x n + 1 for n = 1, 2, 3, . . . . Show that Eustace would obtain the correct value of I(Â¯) , where cos Â¯ = -1 6 . Find all values of Â® for which he would obtain the correct value of I(Â®).

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