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# 11 x1 t08 04 double angles (2013)

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• 1. Double Angles
• 2. Double Angles sin 2 sin   
• 3. Double Angles sin 2 sin   sin cos cos sin    
• 4. Double Angles sin 2 sin   sin cos cos sin    sin 2 2sin cos  
• 5. Double Angles sin 2 sin   sin cos cos sin    sin 2 2sin cos   cos2 cos   
• 6. Double Angles sin 2 sin   sin cos cos sin    sin 2 2sin cos   cos2 cos   cos cos sin sin    
• 7. Double Angles sin 2 sin   sin cos cos sin    sin 2 2sin cos   cos2 cos   cos cos sin sin    2 2cos2 cos sin   
• 8. Double Angles sin 2 sin   sin cos cos sin    sin 2 2sin cos   cos2 cos   cos cos sin sin    2 2cos2 cos sin    2 2cos 1 cos   
• 9. Double Angles sin 2 sin   sin cos cos sin    sin 2 2sin cos   cos2 cos   cos cos sin sin    2 2cos2 cos sin    2 2cos 1 cos   2cos2 2cos 1  
• 10. Double Angles sin 2 sin   sin cos cos sin    sin 2 2sin cos   cos2 cos   cos cos sin sin    2 2cos2 cos sin    2 2cos 1 cos   2cos2 2cos 1   22 1 sin 1  
• 11. Double Angles sin 2 sin   sin cos cos sin    sin 2 2sin cos   cos2 cos   cos cos sin sin    2 2cos2 cos sin    2 2cos 1 cos   2cos2 2cos 1   22 1 sin 1  2cos2 1 2sin  
• 12. Double Angles sin 2 sin   sin cos cos sin    sin 2 2sin cos   cos2 cos   cos cos sin sin    2 2cos2 cos sin    2 2cos 1 cos   2cos2 2cos 1   22 1 sin 1  2cos2 1 2sin   tan 2 tan   
• 13. Double Angles sin 2 sin   sin cos cos sin    sin 2 2sin cos   cos2 cos   cos cos sin sin    2 2cos2 cos sin    2 2cos 1 cos   2cos2 2cos 1   22 1 sin 1  2cos2 1 2sin   tan 2 tan   tan tan1 tan tan  
• 14. Double Angles sin 2 sin   sin cos cos sin    sin 2 2sin cos   cos2 cos   cos cos sin sin    2 2cos2 cos sin    2 2cos 1 cos   2cos2 2cos 1   22 1 sin 1  2cos2 1 2sin   tan 2 tan   tan tan1 tan tan  22tantan 21 tan
• 15. Double Angles  cossin22sin 
• 16. Double Angles  cossin22sin  22sincos2cos 
• 17. Double Angles  cossin22sin  22sincos2cos 1cos2 2 
• 18. Double Angles  cossin22sin  22sincos2cos 1cos2 2    2cos121cos2
• 19. Double Angles  cossin22sin  22sincos2cos 1cos2 2    2cos121cos22sin21
• 20. Double Angles  cossin22sin  22sincos2cos 1cos2 2    2cos121cos22sin21   2cos121sin2
• 21. Double Angles  cossin22sin  22sincos2cos 1cos2 2    2cos121cos22sin21   2cos121sin2 2tan1tan22tan
• 22. Double Angles  cossin22sin  22sincos2cos 1cos2 2    2cos121cos22sin21   2cos121sin2 2tan1tan22tan 2e.g. i If cos , find tan 23 
• 23. Double Angles  cossin22sin  22sincos2cos 1cos2 2    2cos121cos22sin21   2cos121sin2 2tan1tan22tan 2e.g. i If cos , find tan 23 235
• 24. Double Angles  cossin22sin  22sincos2cos 1cos2 2    2cos121cos22sin21   2cos121sin2 2tan1tan22tan 2e.g. i If cos , find tan 23 235 2tan1tan22tan
• 25. Double Angles  cossin22sin  22sincos2cos 1cos2 2    2cos121cos22sin21   2cos121sin2 2tan1tan22tan 2e.g. i If cos , find tan 23 235 2tan1tan22tan 2522tan 2512      
• 26. Double Angles  cossin22sin  22sincos2cos 1cos2 2    2cos121cos22sin21   2cos121sin2 2tan1tan22tan 2e.g. i If cos , find tan 23 235 2tan1tan22tan 2522tan 2512      5144 5 
• 27.  5 5ii Find the exact value of sin cos12 12 
• 28.  5 5ii Find the exact value of sin cos12 12 5 5sin cos12 12  1 5 5= 2sin cos2 12 12    
• 29.  5 5ii Find the exact value of sin cos12 12 5 5sin cos12 12  1 5 5= 2sin cos2 12 12    1 5= sin 22 12   
• 30.  5 5ii Find the exact value of sin cos12 12 5 5sin cos12 12  1 5 5= 2sin cos2 12 12    1 5= sin 22 12   1 5= sin2 6
• 31.  5 5ii Find the exact value of sin cos12 12 5 5sin cos12 12  1 5 5= 2sin cos2 12 12    1 5= sin 22 12   1 5= sin2 61 1=2 21=4
• 32.  2iii If cos , find the exact value of sin3 2 
• 33.  2iii If cos , find the exact value of sin3 2  2 1sin 1 cos22  
• 34.  2iii If cos , find the exact value of sin3 2  2 1sin 1 cos22   2 1sin 1 cos2 2  
• 35.  2iii If cos , find the exact value of sin3 2  2 1sin 1 cos22   2 1sin 1 cos2 2  1 212 3    
• 36.  2iii If cos , find the exact value of sin3 2  2 1sin 1 cos22   2 1sin 1 cos2 2  1 212 3    16
• 37.  2iii If cos , find the exact value of sin3 2  2 1sin 1 cos22   2 1sin 1 cos2 2  1 212 3    161sin2 6 
• 38.  1 cos2iv Prove tan1 cos2xxx
• 39.  1 cos2iv Prove tan1 cos2xxx1 cos21 cos2xx  221 1 2sin1 2cos 1xx  
• 40.  1 cos2iv Prove tan1 cos2xxx1 cos21 cos2xx  221 1 2sin1 2cos 1xx  222sin2cosxx
• 41.  1 cos2iv Prove tan1 cos2xxx1 cos21 cos2xx  221 1 2sin1 2cos 1xx  222sin2cosxx22sincosxx
• 42.  1 cos2iv Prove tan1 cos2xxx1 cos21 cos2xx  221 1 2sin1 2cos 1xx  222sin2cosxx22sincosxx2tan x
• 43.  1 cos2iv Prove tan1 cos2xxx1 cos21 cos2xx  221 1 2sin1 2cos 1xx  222sin2cosxx22sincosxx2tan xtan x
• 44. 1996 Extension 1 HSC Q4a)sin3 cos3(v) Prove that 2sin cos   
• 45. 1996 Extension 1 HSC Q4a)sin3 cos3(v) Prove that 2sin cos   sin3 cos3sin cos  sin3 cos cos3 sinsin cos    
• 46. 1996 Extension 1 HSC Q4a)sin3 cos3(v) Prove that 2sin cos   sin3 cos3sin cos   cossin23sin2 sin3 cos cos3 sinsin cos    
• 47. 1996 Extension 1 HSC Q4a)sin3 cos3(v) Prove that 2sin cos   sin3 cos3sin cos   cossin23sin2 2sin2sin2sin3 cos cos3 sinsin cos    
• 48. 1996 Extension 1 HSC Q4a)sin3 cos3(v) Prove that 2sin cos   sin3 cos3sin cos   cossin23sin2 2sin2sin22sin3 cos cos3 sinsin cos    
• 49. 1994 Extension 1 HSC Q2a)2(vi) Prove the following identity;2tansin 21 tanAAA
• 50. 1994 Extension 1 HSC Q2a)2(vi) Prove the following identity;2tansin 21 tanAAA22tan1 tanAA222sincossin1cosAAAA
• 51. 1994 Extension 1 HSC Q2a)2(vi) Prove the following identity;2tansin 21 tanAAA22tan1 tanAAAAAA22sincoscossin2222sincossin1cosAAAA
• 52. 1994 Extension 1 HSC Q2a)2(vi) Prove the following identity;2tansin 21 tanAAA22tan1 tanAAAAAA22sincoscossin212sin A222sincossin1cosAAAA
• 53. 1994 Extension 1 HSC Q2a)2(vi) Prove the following identity;2tansin 21 tanAAA22tan1 tanAAAAAA22sincoscossin212sin AA2sin222sincossin1cosAAAA
• 54. 1994 Extension 1 HSC Q2a)2(vi) Prove the following identity;2tansin 21 tanAAA22tan1 tanAAAAAA22sincoscossin212sin AA2sin222sincossin1cosAAAABook2Exercise 2A; 2ade, 3bde, 5adej, 7, 8adg, 10ab, 11, 13ck, 16, 19*