11X1 T07 08 products to sums etc (2011)

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<ul><li> 1. Products to Sums</li></ul> <p> 2. Products to Sums 2sin A cos B sin A B sin A B 3. Products to Sums 2sin A cos B sin A B sin A B 2cos A cos B cos A B cos A B 4. Products to Sums 2sin A cos B sin A B sin A B 2cos A cos B cos A B cos A B 2sin A sin B cos A B cos A B 5. Products to Sums2sin A cos B sin A B sin A B 2cos A cos B cos A B cos A B 2sin A sin B cos A B cos A B eg (i) Express as a sum or difference of trig functions 6. Products to Sums2sin A cos B sin A B sin A B 2cos A cos B cos A B cos A B 2sin A sin B cos A B cos A B eg (i) Express as a sum or difference of trig functions a ) 2cos5 x sin x 7. Products to Sums2sin A cos B sin A B sin A B 2cos A cos B cos A B cos A B 2sin A sin B cos A B cos A B eg (i) Express as a sum or difference of trig functions a ) 2cos5 x sin x 2sin x cos5 x 8. Products to Sums2sin A cos B sin A B sin A B 2cos A cos B cos A B cos A B 2sin A sin B cos A B cos A B eg (i) Express as a sum or difference of trig functions a ) 2cos5 x sin x 2sin x cos5 x sin x 5 x sin x 5 x 9. Products to Sums2sin A cos B sin A B sin A B 2cos A cos B cos A B cos A B 2sin A sin B cos A B cos A B eg (i) Express as a sum or difference of trig functions a ) 2cos5 x sin x 2sin x cos5 x sin x 5 x sin x 5 x sin 6 x sin 4 x 10. Products to Sums2sin A cos B sin A B sin A B 2cos A cos B cos A B cos A B 2sin A sin B cos A B cos A B eg (i) Express as a sum or difference of trig functions a ) 2cos5 x sin x 2sin x cos5 x sin x 5 x sin x 5 x sin 6 x sin 4 x sin 6 x sin 4 x 11. Products to Sums2sin A cos B sin A B sin A B 2cos A cos B cos A B cos A B 2sin A sin B cos A B cos A B eg (i) Express as a sum or difference of trig functions a ) 2cos5 x sin x 2sin x cos5 x sin x 5 x sin x 5 x sin 6 x sin 4 x sin 6 x sin 4 x b) cos3 cos5 12. Products to Sums2sin A cos B sin A B sin A B 2cos A cos B cos A B cos A B 2sin A sin B cos A B cos A B eg (i) Express as a sum or difference of trig functions a ) 2cos5 x sin x 2sin x cos5 x sin x 5 x sin x 5 x sin 6 x sin 4 x sin 6 x sin 4 x 1 b) cos3 cos5 2cos3 cos5 2 13. Products to Sums2sin A cos B sin A B sin A B 2cos A cos B cos A B cos A B 2sin A sin B cos A B cos A B eg (i) Express as a sum or difference of trig functions a ) 2cos5 x sin x 2sin x cos5 x sin x 5 x sin x 5 x sin 6 x sin 4 x sin 6 x sin 4 x 1 b) cos3 cos5 2cos3 cos5 21 cos 3 5 cos 3 5 2 14. Products to Sums2sin A cos B sin A B sin A B 2cos A cos B cos A B cos A B 2sin A sin B cos A B cos A B eg (i) Express as a sum or difference of trig functions a ) 2cos5 x sin x 2sin x cos5 x sin x 5 x sin x 5 x sin 6 x sin 4 x sin 6 x sin 4 x 1 b) cos3 cos5 2cos3 cos5 21 cos 3 5 cos 3 5 21 cos8 cos 2 2 15. Products to Sums2sin A cos B sin A B sin A B 2cos A cos B cos A B cos A B 2sin A sin B cos A B cos A B eg (i) Express as a sum or difference of trig functions a ) 2cos5 x sin x 2sin x cos5 x sin x 5 x sin x 5 x sin 6 x sin 4 x sin 6 x sin 4 x 1 b) cos3 cos5 2cos3 cos5 21 cos 3 5 cos 3 5 211 cos8 cos 2 cos8 cos 2 22 16. (ii) Evaluate 2sin 45 cos15 17. (ii) Evaluate 2sin 45 cos15 sin 45 15 sin 45 15 18. (ii) Evaluate 2sin 45 cos15 sin 45 15 sin 45 15 sin 60 sin 30 19. (ii) Evaluate 2sin 45 cos15 sin 45 15 sin 45 15 sin 60 sin 303 1 2 2 20. (ii) Evaluate 2sin 45 cos15 sin 45 15 sin 45 15 sin 60 sin 303 1 2 2 3 1 2 21. (ii) Evaluate 2sin 45 cos15 sin 45 15 sin 45 15 sin 60 sin 303 1 2 2 3 1 2Sums to Products 22. (ii) Evaluate 2sin 45 cos15 sin 45 15 sin 45 15 sin 60 sin 30 3 1 2 23 1 2 Sums to Products1 1sin A sin B 2sin A B cos A B 2 2 23. (ii) Evaluate 2sin 45 cos15 sin 45 15 sin 45 15 sin 60 sin 30 3 1 2 23 1 2 Sums to Products1 1sin A sin B 2sin A B cos A B (2 sine half sum cos half diff)2 2 24. (ii) Evaluate 2sin 45 cos15 sin 45 15 sin 45 15 sin 60 sin 303 1 2 2 3 1 2Sums to Products1 1sin A sin B 2sin A B cos A B (2 sine half sum cos half diff)2 21 1cos A cos B 2cos A B cos A B 2 2 25. (ii) Evaluate 2sin 45 cos15 sin 45 15 sin 45 15 sin 60 sin 303 1 2 2 3 1 2Sums to Products1 1sin A sin B 2sin A B cos A B (2 sine half sum cos half diff)2 21 1cos A cos B 2cos A B cos A B (2 cos half sum cos half diff)2 2 26. (ii) Evaluate 2sin 45 cos15 sin 45 15 sin 45 15 sin 60 sin 303 1 2 2 3 1 2Sums to Products1 1sin A sin B 2sin A B cos A B (2 sine half sum cos half diff)2 21 1cos A cos B 2cos A B cos A B (2 cos half sum cos half diff)2 2 1 1cos A cos B 2sin A B sin A B 2 2 27. (ii) Evaluate 2sin 45 cos15 sin 45 15 sin 45 15 sin 60 sin 303 1 2 2 3 1 2Sums to Products1 1sin A sin B 2sin A B cos A B (2 sine half sum cos half diff)2 21 1cos A cos B 2cos A B cos A B (2 cos half sum cos half diff)2 2 1 1cos A cos B 2sin A B sin A B (minus 2 sine half sum 2 2sine half diff) 28. eg (i) Convert into products of trig functions 29. eg (i) Convert into products of trig functionsa ) cos3 A cos5 A 30. eg (i) Convert into products of trig functions1 1 a ) cos3 A cos5 A 2sin 8 A sin 2 A 2 2 31. eg (i) Convert into products of trig functions11 a ) cos3 A cos5 A 2sin 8 A sin 2 A 22 2sin 4 A sin A 32. eg (i) Convert into products of trig functions11 a ) cos3 A cos5 A 2sin 8 A sin 2 A 22 2sin 4 A sin A 2sin 4 A sin A 33. eg (i) Convert into products of trig functions11 a ) cos3 A cos5 A 2sin 8 A sin 2 A 22 2sin 4 A sin A 2sin 4 A sin A b) sin 6 x sin 4 x 34. eg (i) Convert into products of trig functions11 a ) cos3 A cos5 A 2sin 8 A sin 2 A 22 2sin 4 A sin A 2sin 4 A sin A b) sin 6 x sin 4 x sin 6 x sin 4 x 35. eg (i) Convert into products of trig functions11 a ) cos3 A cos5 A 2sin 8 A sin 2 A 22 2sin 4 A sin A 2sin 4 A sin A b) sin 6 x sin 4 x sin 6 x sin 4 x 11 2sin 2 x cos 10 x 22 36. eg (i) Convert into products of trig functions11 a ) cos3 A cos5 A 2sin 8 A sin 2 A 22 2sin 4 A sin A 2sin 4 A sin A b) sin 6 x sin 4 x sin 6 x sin 4 x 11 2sin 2 x cos 10 x 22 2sin x cos5 x 37. eg (i) Convert into products of trig functions11 a ) cos3 A cos5 A 2sin 8 A sin 2 A 22 2sin 4 A sin A 2sin 4 A sin Ab) sin 6 x sin 4 x sin 6 x sin 4 x 11 2sin 2 x cos 10 x 22 2sin x cos5 x (ii) Solve sin x sin 3 x 0 0 x 360 38. eg (i) Convert into products of trig functions11 a ) cos3 A cos5 A 2sin 8 A sin 2 A 22 2sin 4 A sin A 2sin 4 A sin Ab) sin 6 x sin 4 x sin 6 x sin 4 x 11 2sin 2 x cos 10 x 22 2sin x cos5 x (ii) Solve sin x sin 3 x 0 0 x 360 2sin 2 x cos x 0 39. eg (i) Convert into products of trig functions11 a ) cos3 A cos5 A 2sin 8 A sin 2 A 22 2sin 4 A sin A 2sin 4 A sin Ab) sin 6 x sin 4 x sin 6 x sin 4 x 11 2sin 2 x cos 10 x 22 2sin x cos5 x (ii) Solve sin x sin 3 x 0 0 x 360 2sin 2 x cos x 02sin 2 x cos x 0 40. eg (i) Convert into products of trig functions11 a ) cos3 A cos5 A 2sin 8 A sin 2 A 22 2sin 4 A sin A 2sin 4 A sin Ab) sin 6 x sin 4 x sin 6 x sin 4 x 11 2sin 2 x cos 10 x 22 2sin x cos5 x (ii) Solve sin x sin 3 x 0 0 x 360 2sin 2 x cos x 02sin 2 x cos x 0 sin 2 x 0orcos x 0 41. eg (i) Convert into products of trig functions11 a ) cos3 A cos5 A 2sin 8 A sin 2 A 22 2sin 4 A sin A 2sin 4 A sin Ab) sin 6 x sin 4 x sin 6 x sin 4 x 11 2sin 2 x cos 10 x 22 2sin x cos5 x (ii) Solve sin x sin 3 x 0 0 x 3602sin 2 x cos x 0 2sin 2 x cos x 0sin 2 x 0orcos x 0 2 x 0 ,180 ,360 ,540 ,720 42. eg (i) Convert into products of trig functions11 a ) cos3 A cos5 A 2sin 8 A sin 2 A 22 2sin 4 A sin A 2sin 4 A sin Ab) sin 6 x sin 4 x sin 6 x sin 4 x 11 2sin 2 x cos 10 x 22 2sin x cos5 x (ii) Solve sin x sin 3 x 0 0 x 3602sin 2 x cos x 0 2sin 2 x cos x 0sin 2 x 0orcos x 0 2 x 0 ,180 ,360 ,540 ,720 x 0 ,90 ,180 , 270 ,360 43. eg (i) Convert into products of trig functions11 a ) cos3 A cos5 A 2sin 8 A sin 2 A 22 2sin 4 A sin A 2sin 4 A sin Ab) sin 6 x sin 4 x sin 6 x sin 4 x 11 2sin 2 x cos 10 x 22 2sin x cos5 x (ii) Solve sin x sin 3 x 0 0 x 3602sin 2 x cos x 0 2sin 2 x cos x 0sin 2 x 0orcos x 0 2 x 0 ,180 ,360 ,540 ,720x 90 , 270 x 0 ,90 ,180 , 270 ,360 44. eg (i) Convert into products of trig functions11 a ) cos3 A cos5 A 2sin 8 A sin 2 A 22 2sin 4 A sin A 2sin 4 A sin Ab) sin 6 x sin 4 x sin 6 x sin 4 x 11 2sin 2 x cos 10 x 22 2sin x cos5 x (ii) Solve sin x sin 3 x 0 0 x 3602sin 2 x cos x 0 2sin 2 x cos x 0sin 2 x 0orcos x 0 2 x 0 ,180 ,360 ,540 ,720x 90 , 270 x 0 ,90 ,180 , 270 ,360 x 0 ,90 ,180 , 270 ,360 45. Exercise 2F; 1b, 2b, 3a, 9, 10ace</p>