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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*