[Jan 2007 Q8] 8. (i) Prove that sec2 cosec2 tan2 cot2 x x x x. – – (3) (ii) Given that = arccos 1 and 0 , y x, x y –1 (a) express arcsin in terms of x y. (2) (b) Hence evaluate arccos + arcsin Give your answer in terms of . (1) x x. [June 2006 Q6] 9. (a) Using sin2 + cos2 1, show that the cosec2 cot2 1. – (2) (b) Hence, or otherwise, prove that cosec4 cot4 cosec2 + cot2 . – (2) (c) for 90 < < 180, cosec4 cot4 = 2 cot . – – (6) Mark Schemes Question 1 Question 2
[Jan 2007 Q8] 8. (i) Prove that sec2 x – cosec2 x tan2 x – cot2 x. (3) (ii) Given that y = arccos x, –1 x 1 and 0 y , (a) express arcsin x in terms of y. (2) (b) Hence evaluate arccos x + arcsin x. Give your answer in terms of . (1) [June 2006 Q6] 9. (a) Using sin2 + cos2 1, show that the cosec2 – cot2 1. (2) (b) Hence, or otherwise, prove that cosec4 – cot4 cosec2 + cot2 . (2) (c) for 90 < < 180, cosec4 – cot4 = 2 – cot . (6) Mark Schemes Question 1 Question 2
C3-Chp6-TrigExamQuestions.docx