Hi, there's question 3, it is foundation level, please write down the solution and final answer

[Total : 25 Marks] 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. d 400 400 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]