need answers of the following with working

Question 11 Prove the following identities. sin(A - B) COS(A - B) sin A i. sin B COS B sin Bcos B sin 2.x cot x ii. - COS 2.x (6 + 5 marks) Question 12 Solve the following equations for x, if 0 S x S 2x. i. 3csc x - 4 = 0 ii. 4cos' x + 2cosx - 2 = 0 (6 + 7 marks) Question 13 A function is defined as f(x) = 9cosx + 4sinx. i. Express the function above in the form f(x) = Rcos(x + 6). where O is an acute angle in radians. ii. Solve the equation 9cosx + 4sinx = -5 60 5 0 s 2x. (4 + 7 marks) Question 14 i. Given that A * - vi , where x and y are real constants, prove that x + vi 1 + A 2A ii. If z = 5 - i andw = -2 + 3/. show that (z] = 2|wf (8 + 5 marks) Question 15 i. Write z = - 2i in polar form. ii. find the value of z' and leave the answer in the form a + bi. iii. find the cubic root z = - 2/ and leave the answer in the form a + bi. (4 + 4 + 6 marks) Question 16 Two complex numbers a = 8 cos -# + isin- and B = 4 cos ~ + isin ~ are given Evaluate the following and leave the answer in the form a + bi. i. ii. arg iii. Ba (4 + 1 + 1 marks) The End