Hi, here's questions 3 and 4, please help me answer with fully worked solutions and write down the final answer, these 2 questions are in foundation level

Question 3 (a) Prove that (i) tan(2x) = 2sinxcosx 2cos2x-1 (4 marks) (ii) (1 + cos x) (1 + cot2 x) (1 - cos x) = 1 (4 marks) (b) An airplane is flying in a straight line towards an airfield at a fixed altitude. The angle of depression to the airfield is 350. After flying 3 more miles the angle of depression is 570. What is the distance between the airplane and the airfield when the angle is 570? (4 marks) (c) Consider a triangle in the coordinate plane where the coordinates of the vertices are A(2,1), B(4,-5) and C(-3,-7). Find (i) The perimeter of the triangle (4 marks) (ii) Area of the triangle (3 marks) Approximate the answers to 2 decimal places. (d) A drawbridge is 80-meter-long when stretched across a river. As shown in the figure below, the two sections of the bridge can be rotated upward through an angle of 40. 409 40 80m Page 2 of 3 May-Aug. 2020 Final Assessment MF005 Algebra & Trigonometry (i) If the water level is 15 meter below the closed bridge, approximate the distance d between the end of a section and the water level when the bridge is fully open. (3 marks) (ii) Approximately how far apart are the ends of the two sections when the bridge is fully opened. (refer to g in the figure) (3 marks) [Total : 25 Marks] Question 4 (a) Find a in the form of x + iy, if = = = + , provided that b = -2 + 4i and c = 2 + i. (6 marks) (b) Given the complex numbers, u = 4 - 2i and v = 3 + i. Express w = , in the form x + yi, where x and y are real numbers. (5 marks) (c) Consider the complex number z = a + bi, where the modulus of z is 6 and the argument of z is , (i) the values of a and b (2 marks) (ii) the value of |z2| (3 marks) (d) Given that z1 = 5 + 2i and z2 = 2 - 3i, express -in polar (trigonometric) form. (5 marks) (e) Use De Moivre's theorem to express (- 13 - zi) in the form a + bi, where a and b are real numbers. (4 marks) [Total : 25 marks]