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SUEC 高中 Adv Maths (Product-Sum Indentities)
- 1. 𝒑𝒈 𝟐𝟔𝟐 𝑐𝑜𝑠 (𝑎 + 𝑏) + 𝑐𝑜𝑠 (𝑎 − 𝑏) = 2 𝑐𝑜𝑠 𝑎 𝑐𝑜𝑠 𝑏
- 2. 𝒑𝒈 𝟐𝟔𝟑
- 4. = 𝟑 𝟑 = 𝑠𝑖𝑛 10 ° 𝑠𝑖𝑛 50 ° 𝑠𝑖𝑛 70 ° 𝑐𝑜𝑠 10 ° 𝑐𝑜𝑠 50 ° 𝑐𝑜𝑠 70 ° = 𝑐𝑜𝑠 10 ° 𝑐𝑜𝑠 10 ° × 𝑠𝑖𝑛 10 ° 𝑠𝑖𝑛 50 ° 𝑠𝑖𝑛 70 ° 𝑐𝑜𝑠 10 ° 𝑐𝑜𝑠 50 ° 𝑐𝑜𝑠 70 ° = 1 2 𝑠𝑖𝑛 20 ° 𝑐𝑜𝑠 20 ° 𝑠𝑖𝑛 50 ° 1 2 𝑐𝑜𝑠 10 ° (𝑐𝑜𝑠 40 ° + 𝑐𝑜𝑠 60 °) 𝑐𝑜𝑠 70° = 1 4 𝑠𝑖𝑛 40 ° 𝑠𝑖𝑛 50 ° 1 2 𝑐𝑜𝑠 10 ° (𝑐𝑜𝑠 40 ° 𝑐𝑜𝑠 70 ° + 1 2 𝑐𝑜𝑠 70 °) = 1 8 𝑐𝑜𝑠 10 ° − 𝑐𝑜𝑠 90 ° 1 4 𝑐𝑜𝑠 10° 𝑐𝑜𝑠 30° + 𝑐𝑜𝑠 110° + 𝑐𝑜𝑠 70 ° = 1 2 3 2 − 𝑐𝑜𝑠 70° + 𝑐𝑜𝑠 70 °
- 5. 𝒑𝒈 𝟐𝟔𝟑
- 6. 𝒑𝒈 𝟐𝟔𝟒 𝑠𝑖𝑛 4𝜃 + 𝑠𝑖𝑛 2𝜃 𝑠𝑖𝑛 9𝜃 − 𝑠𝑖𝑛 3𝜃 − 𝑐𝑜𝑠 12𝜃 + 𝑐𝑜𝑠 6𝜃 − 1 2 (𝑐𝑜𝑠 4 ∝ − 𝑐𝑜𝑠 2 ∝) 1 2 (𝑠𝑖𝑛 120 ° − 𝑠𝑖𝑛 2 ∝)
- 7. 𝒑𝒈 𝟐𝟔𝟑
- 8. 𝒑𝒈 𝟐𝟔𝟑
- 9. 𝒑𝒈 𝟐𝟔𝟓
- 10. 𝒑𝒈 𝟐𝟔𝟓 𝑠𝑖𝑛 20 ° 𝑠𝑖𝑛 40 ° 𝑠𝑖𝑛 80 ° = 1 2 𝑐𝑜𝑠 20 ° − 𝑐𝑜𝑠 60 ° 𝑠𝑖𝑛 80 ° = 1 2 𝑐𝑜𝑠 20 ° − 1 2 𝑠𝑖𝑛 80 ° = 1 4 2 𝑐𝑜𝑠 20 ° − 1 𝑠𝑖𝑛 80 ° = 1 4 2 𝑐𝑜𝑠 20 ° 𝑠𝑖𝑛 80 ° − 𝑠𝑖𝑛 80 ° = 1 4 𝑠𝑖𝑛 100 ° − 𝑠𝑖𝑛 60 ° − 𝑠𝑖𝑛 80 ° = 1 4 𝑠𝑖𝑛 80 ° − 3 2 − 𝑠𝑖𝑛 80 ° = 1 8 3 𝑐𝑜𝑠 4𝑥 𝑐𝑜𝑠 2𝑥 − 𝑐𝑜𝑠2 3𝑥 = 1 2 𝑐𝑜𝑠 2𝑥 + 𝑐𝑜𝑠 6𝑥 − 𝑐𝑜𝑠2 3𝑥 = 1 2 1 − 2𝑠𝑖𝑛 2 𝑥 + 2 𝑐𝑜𝑠2 3𝑥 − 1 − 𝑐𝑜𝑠2 3𝑥 = − 𝑠𝑖𝑛 2 𝑥
- 11. 𝒑𝒈 𝟐𝟔𝟓 4 𝑐𝑜𝑠 𝐴 𝑐𝑜𝑠 (60° + 𝐴) 𝑐𝑜𝑠 (60° − 𝐴) = 2 𝑐𝑜𝑠 𝐴 (𝑐𝑜𝑠 2𝐴 + 𝑐𝑜𝑠 120 °) = 2 𝑐𝑜𝑠 𝐴 (𝑐𝑜𝑠 2𝐴 − 𝑐𝑜𝑠 60 °) = 2 𝑐𝑜𝑠 𝐴 𝑐𝑜𝑠 2𝐴 − 1 2 = 2 𝑐𝑜𝑠 𝐴 𝑐𝑜𝑠 2𝐴 − 𝑐𝑜𝑠 𝐴 = 𝑐𝑜𝑠 𝐴 + 𝑐𝑜𝑠 3𝐴 − 𝑐𝑜𝑠 𝐴 = 𝑐𝑜𝑠 3𝐴
- 12. 𝒑𝒈 𝟐𝟔𝟓 − 𝟐𝟔𝟔
- 13. 𝒑𝒈 𝟐𝟔𝟔
- 14. 𝒑𝒈 𝟐𝟔𝟔 − 𝟐𝟔𝟕
- 15. 𝒑𝒈 𝟐𝟔𝟗 𝟐 𝒔𝒊𝒏 𝟔𝜽 𝒄𝒐𝒔 𝟐𝜽 − 𝟐 𝒔𝒊𝒏 𝟑𝜶 𝒔𝒊𝒏 𝟐𝜶 𝟐 𝒄𝒐𝒔 𝟏𝟏𝑨 𝟐 𝒄𝒐𝒔 𝟕𝑨 𝟐 𝟐 𝒄𝒐𝒔 𝟔𝜽 𝒔𝒊𝒏 𝜽 𝟐 𝒄𝒐𝒔 𝟒𝟓 ° + 𝜶 𝟐 𝒄𝒐𝒔 𝟒𝟓 ° − 𝜶 𝟐
- 16. 𝒑𝒈 𝟐𝟔𝟕
- 18. 𝒑𝒈 𝟐𝟔𝟕
- 19. 𝒑𝒈 𝟐𝟔𝟕
- 20. 𝒑𝒈 𝟐𝟕𝟎
- 21. 𝒑𝒈 𝟐𝟕𝟎
- 22. 𝒑𝒈 𝟐𝟕𝟎 𝑐𝑜𝑠2𝐴 + 𝑐𝑜𝑠2 (60 °−) + 𝑐𝑜𝑠2 (60 ° + 𝐴) = 𝑐𝑜𝑠2 𝐴 + 1 2 𝑐𝑜𝑠 120 ° − 2𝐴 + 1 + 1 2 𝑐𝑜𝑠 120 ° + 2𝐴 + 1 𝑐𝑜𝑠2 𝐴 = 𝑐𝑜𝑠 2𝐴 + 1 2 = 𝑐𝑜𝑠2 𝐴 + 1 + 1 2 𝑐𝑜𝑠 120 ° − 2𝐴 + 𝑐𝑜𝑠 120 ° + 2𝐴 = 𝑐𝑜𝑠2𝐴 + 1 + 𝑐𝑜𝑠 120 ° 𝑐𝑜𝑠 2𝐴 = 𝑐𝑜𝑠2 𝐴 + 1 − 1 2 (2𝑐𝑜𝑠2 𝐴 − 1) = 𝑐𝑜𝑠2 𝐴 + 1 − 𝑐𝑜𝑠2 𝐴 + 1 2 = 3 2
- 23. 𝒑𝒈 𝟐𝟔𝟖 𝐴 + 𝐵 + 𝐶 = 180 𝐴 + 𝐵 2 = 90 − 𝐶 2 𝑠𝑖𝑛 𝐴 + 𝐵 2 = 𝑠𝑖𝑛 90 − 𝐶 2 = 𝑐𝑜𝑠 𝐶 2
- 24. 𝒑𝒈 𝟐𝟔𝟖 − 𝟐𝟔𝟗 𝐴 + 𝐵 + 𝐶 = 180 𝐴 + 𝐵 2 = 90 − 𝐶 2 𝑐𝑜𝑠 𝐴 + 𝐵 2 = 𝑐𝑜𝑠 90 − 𝐶 2 = 𝑠𝑖𝑛 𝐶 2
- 25. 𝒑𝒈 𝟐𝟔𝟗 𝐴 + 𝐵 + 𝐶 = 180 𝐴 + 𝐵 2 = 90 − 𝐶 2 𝑐𝑜𝑠 𝐴 + 𝐵 2 = 𝑐𝑜𝑠 90 − 𝐶 2 = 𝑠𝑖𝑛 𝐶 2
- 26. 𝒑𝒈 𝟐𝟕𝟎
Editor's Notes
- https://www.onlinemathlearning.com/trig-functions.html
- turn into sum or diff
- 16 ans - behind the book