11 x1 t04 14 products to sums etc
DESCRIPTION
TRANSCRIPT
![Page 1: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/1.jpg)
Products to Sums
![Page 2: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/2.jpg)
Products to Sums 2sin cos sin sinA B A B A B
![Page 3: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/3.jpg)
Products to Sums 2sin cos sin sinA B A B A B
2cos cos cos cosA B A B A B
![Page 4: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/4.jpg)
Products to Sums 2sin cos sin sinA B A B A B
2cos cos cos cosA B A B A B
2sin sin cos cosA B A B A B
![Page 5: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/5.jpg)
Products to Sums 2sin cos sin sinA B A B A B
2cos cos cos cosA B A B A B
2sin sin cos cosA B A B A B
eg (i) Express as a sum or difference of trig functions
![Page 6: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/6.jpg)
Products to Sums 2sin cos sin sinA B A B A B
2cos cos cos cosA B A B A B
2sin sin cos cosA B A B A B
eg (i) Express as a sum or difference of trig functions) 2cos5 sina x x
![Page 7: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/7.jpg)
Products to Sums 2sin cos sin sinA B A B A B
2cos cos cos cosA B A B A B
2sin sin cos cosA B A B A B
eg (i) Express as a sum or difference of trig functions) 2cos5 sina x x 2sin cos5x x
![Page 8: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/8.jpg)
Products to Sums 2sin cos sin sinA B A B A B
2cos cos cos cosA B A B A B
2sin sin cos cosA B A B A B
eg (i) Express as a sum or difference of trig functions) 2cos5 sina x x 2sin cos5x x
sin 5 sin 5x x x x
![Page 9: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/9.jpg)
Products to Sums 2sin cos sin sinA B A B A B
2cos cos cos cosA B A B A B
2sin sin cos cosA B A B A B
eg (i) Express as a sum or difference of trig functions) 2cos5 sina x x 2sin cos5x x
sin 5 sin 5x x x x
sin 6 sin 4x x
![Page 10: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/10.jpg)
Products to Sums 2sin cos sin sinA B A B A B
2cos cos cos cosA B A B A B
2sin sin cos cosA B A B A B
eg (i) Express as a sum or difference of trig functions) 2cos5 sina x x 2sin cos5x x
sin 5 sin 5x x x x
sin 6 sin 4x x sin 6 sin 4x x
![Page 11: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/11.jpg)
Products to Sums 2sin cos sin sinA B A B A B
2cos cos cos cosA B A B A B
2sin sin cos cosA B A B A B
eg (i) Express as a sum or difference of trig functions) 2cos5 sina x x 2sin cos5x x
sin 5 sin 5x x x x
sin 6 sin 4x x sin 6 sin 4x x
) cos3 cos5b
![Page 12: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/12.jpg)
Products to Sums 2sin cos sin sinA B A B A B
2cos cos cos cosA B A B A B
2sin sin cos cosA B A B A B
eg (i) Express as a sum or difference of trig functions) 2cos5 sina x x 2sin cos5x x
sin 5 sin 5x x x x
sin 6 sin 4x x sin 6 sin 4x x
) cos3 cos5b 12cos3 cos5
2
![Page 13: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/13.jpg)
Products to Sums 2sin cos sin sinA B A B A B
2cos cos cos cosA B A B A B
2sin sin cos cosA B A B A B
eg (i) Express as a sum or difference of trig functions) 2cos5 sina x x 2sin cos5x x
sin 5 sin 5x x x x
sin 6 sin 4x x sin 6 sin 4x x
) cos3 cos5b
1cos 3 5 cos 3 5
2
12cos3 cos5
2
![Page 14: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/14.jpg)
Products to Sums 2sin cos sin sinA B A B A B
2cos cos cos cosA B A B A B
2sin sin cos cosA B A B A B
eg (i) Express as a sum or difference of trig functions) 2cos5 sina x x 2sin cos5x x
sin 5 sin 5x x x x
sin 6 sin 4x x sin 6 sin 4x x
) cos3 cos5b
1cos 3 5 cos 3 5
2
1cos8 cos 2
2
12cos3 cos5
2
![Page 15: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/15.jpg)
Products to Sums 2sin cos sin sinA B A B A B
2cos cos cos cosA B A B A B
2sin sin cos cosA B A B A B
eg (i) Express as a sum or difference of trig functions) 2cos5 sina x x 2sin cos5x x
sin 5 sin 5x x x x
sin 6 sin 4x x sin 6 sin 4x x
) cos3 cos5b
1cos 3 5 cos 3 5
2
1cos8 cos 2
2 1
cos8 cos 22
12cos3 cos5
2
![Page 16: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/16.jpg)
(ii) Evaluate 2sin 45 cos15
![Page 17: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/17.jpg)
(ii) Evaluate 2sin 45 cos15 sin 45 15 sin 45 15
![Page 18: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/18.jpg)
(ii) Evaluate 2sin 45 cos15 sin 45 15 sin 45 15
sin 60 sin30
![Page 19: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/19.jpg)
(ii) Evaluate 2sin 45 cos15 sin 45 15 sin 45 15
sin 60 sin30
3 12 2
![Page 20: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/20.jpg)
(ii) Evaluate 2sin 45 cos15 sin 45 15 sin 45 15
sin 60 sin30
3 12 2
3 12
![Page 21: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/21.jpg)
(ii) Evaluate 2sin 45 cos15 sin 45 15 sin 45 15
sin 60 sin30
3 12 2
3 12
Sums to Products
![Page 22: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/22.jpg)
(ii) Evaluate 2sin 45 cos15 sin 45 15 sin 45 15
sin 60 sin30
3 12 2
3 12
Sums to Products 1 1
sin sin 2sin cos2 2
A B A B A B
![Page 23: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/23.jpg)
(ii) Evaluate 2sin 45 cos15 sin 45 15 sin 45 15
sin 60 sin30
3 12 2
3 12
Sums to Products 1 1
sin sin 2sin cos2 2
A B A B A B (2 sine half sum cos half diff)
![Page 24: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/24.jpg)
(ii) Evaluate 2sin 45 cos15 sin 45 15 sin 45 15
sin 60 sin30
3 12 2
3 12
Sums to Products 1 1
sin sin 2sin cos2 2
A B A B A B (2 sine half sum cos half diff)
1 1cos cos 2cos cos
2 2A B A B A B
![Page 25: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/25.jpg)
(ii) Evaluate 2sin 45 cos15 sin 45 15 sin 45 15
sin 60 sin30
3 12 2
3 12
Sums to Products 1 1
sin sin 2sin cos2 2
A B A B A B (2 sine half sum cos half diff)
1 1cos cos 2cos cos
2 2A B A B A B (2 cos half sum cos half diff)
![Page 26: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/26.jpg)
(ii) Evaluate 2sin 45 cos15 sin 45 15 sin 45 15
sin 60 sin30
3 12 2
3 12
Sums to Products 1 1
sin sin 2sin cos2 2
A B A B A B (2 sine half sum cos half diff)
1 1cos cos 2cos cos
2 2A B A B A B (2 cos half sum cos half diff)
1 1cos cos 2sin sin
2 2A B A B A B
![Page 27: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/27.jpg)
(ii) Evaluate 2sin 45 cos15 sin 45 15 sin 45 15
sin 60 sin30
3 12 2
3 12
Sums to Products 1 1
sin sin 2sin cos2 2
A B A B A B (2 sine half sum cos half diff)
1 1cos cos 2cos cos
2 2A B A B A B (2 cos half sum cos half diff)
1 1cos cos 2sin sin
2 2A B A B A B (minus 2 sine half sum
sine half diff)
![Page 28: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/28.jpg)
eg (i) Convert into products of trig functions
![Page 29: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/29.jpg)
eg (i) Convert into products of trig functions
) cos3 cos5a A A
![Page 30: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/30.jpg)
eg (i) Convert into products of trig functions
) cos3 cos5a A A 1 12sin 8 sin 2
2 2A A
![Page 31: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/31.jpg)
eg (i) Convert into products of trig functions
) cos3 cos5a A A 1 12sin 8 sin 2
2 2A A
2sin 4 sinA A
![Page 32: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/32.jpg)
eg (i) Convert into products of trig functions
) cos3 cos5a A A 1 12sin 8 sin 2
2 2A A
2sin 4 sinA A
2sin 4 sinA A
![Page 33: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/33.jpg)
eg (i) Convert into products of trig functions
) cos3 cos5a A A 1 12sin 8 sin 2
2 2A A
2sin 4 sinA A
2sin 4 sinA A
) sin 6 sin 4b x x
![Page 34: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/34.jpg)
eg (i) Convert into products of trig functions
) cos3 cos5a A A 1 12sin 8 sin 2
2 2A A
2sin 4 sinA A
2sin 4 sinA A
) sin 6 sin 4b x x sin 6 sin 4x x
![Page 35: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/35.jpg)
eg (i) Convert into products of trig functions
) cos3 cos5a A A 1 12sin 8 sin 2
2 2A A
2sin 4 sinA A
2sin 4 sinA A
) sin 6 sin 4b x x sin 6 sin 4x x
1 12sin 2 cos 10
2 2x x
![Page 36: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/36.jpg)
eg (i) Convert into products of trig functions
) cos3 cos5a A A 1 12sin 8 sin 2
2 2A A
2sin 4 sinA A
2sin 4 sinA A
) sin 6 sin 4b x x sin 6 sin 4x x
1 12sin 2 cos 10
2 2x x
2sin cos5x x
![Page 37: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/37.jpg)
eg (i) Convert into products of trig functions
) cos3 cos5a A A 1 12sin 8 sin 2
2 2A A
2sin 4 sinA A
2sin 4 sinA A
) sin 6 sin 4b x x sin 6 sin 4x x
1 12sin 2 cos 10
2 2x x
2sin cos5x x(ii) Solve sin sin3 0 0 360x x x
![Page 38: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/38.jpg)
eg (i) Convert into products of trig functions
) cos3 cos5a A A 1 12sin 8 sin 2
2 2A A
2sin 4 sinA A
2sin 4 sinA A
) sin 6 sin 4b x x sin 6 sin 4x x
1 12sin 2 cos 10
2 2x x
2sin cos5x x(ii) Solve sin sin3 0 0 360x x x
2sin 2 cos 0x x
![Page 39: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/39.jpg)
eg (i) Convert into products of trig functions
) cos3 cos5a A A 1 12sin 8 sin 2
2 2A A
2sin 4 sinA A
2sin 4 sinA A
) sin 6 sin 4b x x sin 6 sin 4x x
1 12sin 2 cos 10
2 2x x
2sin cos5x x(ii) Solve sin sin3 0 0 360x x x
2sin 2 cos 0x x 2sin 2 cos 0x x
![Page 40: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/40.jpg)
eg (i) Convert into products of trig functions
) cos3 cos5a A A 1 12sin 8 sin 2
2 2A A
2sin 4 sinA A
2sin 4 sinA A
) sin 6 sin 4b x x sin 6 sin 4x x
1 12sin 2 cos 10
2 2x x
2sin cos5x x(ii) Solve sin sin3 0 0 360x x x
2sin 2 cos 0x x 2sin 2 cos 0x x
sin 2 0 or cos 0x x
![Page 41: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/41.jpg)
eg (i) Convert into products of trig functions
) cos3 cos5a A A 1 12sin 8 sin 2
2 2A A
2sin 4 sinA A
2sin 4 sinA A
) sin 6 sin 4b x x sin 6 sin 4x x
1 12sin 2 cos 10
2 2x x
2sin cos5x x(ii) Solve sin sin3 0 0 360x x x
2sin 2 cos 0x x 2sin 2 cos 0x x
sin 2 0 or cos 0x x 2 0 ,180 ,360 ,540 ,720x
![Page 42: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/42.jpg)
eg (i) Convert into products of trig functions
) cos3 cos5a A A 1 12sin 8 sin 2
2 2A A
2sin 4 sinA A
2sin 4 sinA A
) sin 6 sin 4b x x sin 6 sin 4x x
1 12sin 2 cos 10
2 2x x
2sin cos5x x(ii) Solve sin sin3 0 0 360x x x
2sin 2 cos 0x x 2sin 2 cos 0x x
sin 2 0 or cos 0x x 2 0 ,180 ,360 ,540 ,720x
0 ,90 ,180 ,270 ,360x
![Page 43: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/43.jpg)
eg (i) Convert into products of trig functions
) cos3 cos5a A A 1 12sin 8 sin 2
2 2A A
2sin 4 sinA A
2sin 4 sinA A
) sin 6 sin 4b x x sin 6 sin 4x x
1 12sin 2 cos 10
2 2x x
2sin cos5x x(ii) Solve sin sin3 0 0 360x x x
2sin 2 cos 0x x 2sin 2 cos 0x x
sin 2 0 or cos 0x x 2 0 ,180 ,360 ,540 ,720x
0 ,90 ,180 ,270 ,360x 90 ,270x
![Page 44: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/44.jpg)
eg (i) Convert into products of trig functions
) cos3 cos5a A A 1 12sin 8 sin 2
2 2A A
2sin 4 sinA A
2sin 4 sinA A
) sin 6 sin 4b x x sin 6 sin 4x x
1 12sin 2 cos 10
2 2x x
2sin cos5x x(ii) Solve sin sin3 0 0 360x x x
2sin 2 cos 0x x 2sin 2 cos 0x x
sin 2 0 or cos 0x x 2 0 ,180 ,360 ,540 ,720x
0 ,90 ,180 ,270 ,360x 90 ,270x
0 ,90 ,180 ,270 ,360x
![Page 45: 11 X1 T04 14 Products To Sums Etc](https://reader035.vdocuments.us/reader035/viewer/2022062617/54c9bdb24a7959dc2e8b4600/html5/thumbnails/45.jpg)
Exercise 2F; 1b, 2b, 3a, 9, 10ace