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QUESTION 3 sing (a) Show that = cot-. 1-cos 0 | 4 marks | (C3, CLO3, MQF LOD6) (b) Prove that tan 30_ Stand - tan' o 1-3 tan' 9 [ 5 marks | (C3, CLO3, MQF LOD6) QUESTION 4 (a) Show that the equation cosee 20 -4cot 29 =6 can be reduced to cot* 20-4cot 20-5=0. Hence, solve the equation cosec- 20 -4cot20 =6 for -180' s 0 $180". | 6 marks | (C3, CLO3, MOF LOD6) (b) By using f = tan - , solve the equation cosx-2sinx =1 for (" S x $ 360. [ 6 marks ] (C3, CLO3, MQF LOD6) QUESTION S (a) Express v2 sinx - 2 cos x in the form of Rain(x -a), where R > 0 and OSas- | 4 marks ] (C2, CLO3, MOF LOD6) (b) Solve the equation v2 sin x - V2 cos x =-I for - ASXSx. [3 marks ] (C3, CLO3, MQF LOD6) (c) Find the maximum and minimum values for ()_(2 cos x - v2 sinx) [ 4 marks | (C3, CLO3, MQF LOD6)