Hi,

Can you please help me with these maths questions by showing me the answer with steps. Thank you very much.

Question 2 De Moivre Theorem Write the expressions for Throughout this SAC, you will be using the following equations: a) sin(0 - 4) cis(0) = cos(0) + isin(0) ... ... ... ... .. (1) cis(0) x cis(4) = cis(0 + 4 ) .......... (2) b) cos(0 (cis(@) )" = cis(ne ) . . . . . . .. (3) where i = v-1 and n is a positive integer and all angls are in radians. In addition, you will need to use the following binomial expansions: (A + B) 3 = A3 + 3A2B + 3AB2 + B3 (A + B) 4 = A4 + 4A3B + 6A2B2 + 4AB3 + B4 Question 1 Use equations (1) and (2) to prove the following addition formulas: sin (0 + 4) = sin(0) cos(4) + cos(0)sin(q) cos(0 + 4) = cos(0) cos(4) - sin(0)sin(4) (5 marks) NQuestion 2 Write the expressions for a) sin(0 - 4) (1 mark) b) cos(8 - 4) (1 mark) Question 3 Use the results of Question 2 with suitable values of 0 & 4 to find the exact values of the following. Show your working and give answers with rational denominators. a) sin (2) (3 marks) b) cos () (3 marks) c) tan () (3 marks) 3Question 4 Question 5 Use equations (1) an Use the results of Question 1 with suitable values of 0 & 4 to find the exact values of the following Show your working and give answers with rational denominators. a) sin (") (3 marks) b) cos (3 marks) c) tan () (3 marks)wing Question 5 Use equations (1) and (3) with n = 2 to prove the following double-angle formulas: 3 marks) sin(20) = 2sin(0) cos (0) cos(20) = cos2 (0) - sin2(0) (4 marks) Question 6 Use the results of Question 5 to prove the following. Show your working. a) cos(20) = 2cos2(0) - 1 (2 marks) b) cos(20) = 1 - 2sin2(0) (2 marks)Use the results of Question 7 Question 7 Question 8 Show your working and Use the results of Question 6 to prove the following. Show your working. sin a) a) sin(0) = + 1-cos (20) (2 marks) b) cos(0) = + 1+cos (20) 2 (2 marks) 6Question 8 Use the results of Question 7 to find the exact values of the following. Show your working and give answers with rational denominators. marks) a) sin (2) (3 marks) b) cos (3 marks) c) tan (3 marks)Question 9 Question 10 Compare the results of Questions 3 & 8. Use equations a) Show that the two expressions for sin ( ) are equal. (2 man b) Show that the two expressions for cos () are equal. (2 marks) 8Question 10 (2 marks) Use equations (1) and (3) with n = 3 to prove the following formulas: cos(30) = cos3 (0) - 3sin2(0)cos(0) sin(30) = 3sin(0) cos2(0) - sin3 (0) (6 marks) Question 11 Use the results in Question 10 to find: a) Expression for cos(30) in terms of cos(0) only. (4 marks) b) Expression for sin(30) in terms of sin(0) only. (4 marks) 9