For the first three parts of this question, we will examine different ways of doing the integral: 1 = sins x dx. (a) By using the substitution u = cosx, show that: 1 = - cosx + = cos3 x - = cos x + C [4 marks] (b) Find the power reduction formula for sin x. Use this to show that: 5 1 = - cos 5x + cosx + C 80 48 cos 3x - [6 marks] (c) Use De Moivre's theorem to show that: cos 5x = 16 cos' x - 20 cos x + 5 cosx. Then use this to verify that the expressions in (a) and (b) are the same. You may also use the identity cos 3x = 4 cos3 x - 3cos x without proving it. [6 marks] The last two parts of this question are on the vectors a = 3i + 6j + 2k and b = -8i + 4j + k. (d) What is the angle between a and b? Give your answer in radians to 4 significant digits. [5 marks] (e) Find a unit vector which is perpendicular to both a and b. [4 marks]