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SUEC 高中 Adv Maths (Double-Half Angle Indentities)
- 1. 𝒑𝒈 𝟐𝟓𝟎
- 2. 𝒑𝒈 𝟐𝟓𝟐 0.96 - 0.28 1 1 𝟑 𝟑 4
- 3. 𝒑𝒈 𝟐𝟓𝟏
- 4. 𝒑𝒈 𝟐𝟓𝟏 𝑠𝑖𝑛
- 6. 𝒑𝒈 𝟐𝟓𝟐
- 7. 𝒑𝒈 𝟐𝟓𝟐
- 8. 𝒑𝒈 𝟐𝟓𝟐 𝑐𝑜𝑠4 𝑥 2 − 𝑠𝑖𝑛4 𝑥 2 = 𝑐𝑜𝑠2 𝑥 2 2 − 𝑠𝑖𝑛2 𝑥 2 2 (𝑎 + 𝑏)(𝑎 − 𝑏) = 𝑎2 − 𝑏2 𝑎 = 𝑐𝑜𝑠2 𝑥 2 𝑏 = 𝑠𝑖𝑛2 𝑥 2 = 𝑐𝑜𝑠2 𝑥 2 + 𝑠𝑖𝑛2 𝑥 2 𝑐𝑜𝑠2 𝑥 2 − 𝑠𝑖𝑛2 𝑥 2 = 1 𝑐𝑜𝑠2 𝑥 2 − 𝑠𝑖𝑛2 𝑥 2 = 𝑐𝑜𝑠 𝑥
- 9. 𝒑𝒈 𝟐𝟓𝟑
- 10. 𝒑𝒈 𝟐𝟓𝟑
- 11. 𝒑𝒈 𝟐𝟓𝟑
- 12. 𝒑𝒈 𝟐𝟓𝟑 − 𝟐𝟓𝟒
- 13. 𝒑𝒈 𝟐𝟓𝟒
- 14. 𝒑𝒈 𝟐𝟓𝟓
- 16. 𝒑𝒈 𝟐𝟓𝟕
- 17. 𝒑𝒈 𝟐𝟓𝟕 − 𝟐𝟓𝟖
- 18. 𝒑𝒈 𝟐𝟓𝟖 − 𝟐𝟓𝟗
- 19. 𝒑𝒈 𝟐𝟔𝟏 𝑡2 𝟏 𝒕 𝟏 − 𝑡2 2𝑡2 𝟏 5𝑡2 − 𝟔𝒕 − 𝟑
- 20. 𝒑𝒈 𝟐𝟔𝟎 𝐿𝑒𝑡 𝑡 = 𝑡𝑎𝑛 𝜃
- 21. 𝒑𝒈 𝟐𝟔𝟏 = 𝒎 𝟑𝒏𝟐 − 𝒎𝟐 𝑚2 + 𝑛2 𝐿𝑒𝑡 𝑡 = 𝑡𝑎𝑛 𝛼 2 = 𝑚 𝑛 𝑚 𝑐𝑜𝑠 𝛼 + 𝑛 𝑠𝑖𝑛 𝛼 = 𝑚 1−𝑡2 1+𝑡2 + 𝑛 2𝑡 1+𝑡2 = 𝑚 𝑛2− 𝑚2 𝑛2+𝑚2 + 2𝑚𝑛2 𝑛2+𝑚2 = 𝑚 1− 𝑚 𝑛 2 1+ 𝑚 𝑛 2 + 𝑛 2 𝑚 𝑛 1+ 𝑚 𝑛 2
- 22. 𝒑𝒈 𝟐𝟓𝟓
- 23. 𝒑𝒈 𝟐𝟓𝟓 − 𝟐𝟓𝟔
- 25. 𝒑𝒈 𝟐𝟔𝟏
- 26. 𝒑𝒈 𝟐𝟔𝟏 = 𝑡𝑎𝑛 ∝ + 𝑠𝑒𝑐 ∝ = 𝑡𝑎𝑛 𝜋 4 + 𝑡𝑎𝑛 𝛼 2 1 − 𝑎𝑛 𝜋 4 𝑡𝑎𝑛 𝛼 2 = 1 + 𝑡𝑎𝑛 𝛼 2 1 − 𝑡𝑎𝑛 𝛼 2 = 1 + 𝑠𝑖𝑛 𝛼 2 𝑐𝑜𝑠 𝛼 2 1 − 𝑠𝑖𝑛 𝛼 2 𝑐𝑜𝑠 𝛼 2 = 𝑐𝑜𝑠 𝛼 2 + 𝑠𝑖𝑛 𝛼 2 𝑐𝑜𝑠 𝛼 2 − 𝑠𝑖𝑛 𝛼 2 𝑐𝑜𝑠 𝛼 2 + 𝑠𝑖𝑛 𝛼 2 𝑐𝑜𝑠 𝛼 2 + 𝑠𝑖𝑛 𝛼 2 = 𝑐𝑜𝑠2 ∝ 2 + 2 𝑐𝑜𝑠 𝛼 2 𝑠𝑖𝑛 𝛼 2 + 𝑠𝑖𝑛2 ∝ 2 𝑐𝑜𝑠 ∝ = 1 + 𝑠𝑖𝑛 ∝ 𝑐𝑜𝑠 ∝ 𝑡𝑎𝑛 𝜋 4 + 𝛼 2
- 27. 𝒑𝒈 𝟐𝟔𝟏 − 𝟐𝟔𝟐
- 28. 𝒑𝒈 𝟐𝟔𝟏 − 𝟐𝟔𝟐 = 𝑐𝑜𝑠 ∝ 𝑠𝑖𝑛 𝛼 2 𝑐𝑜𝑠 𝛼 2 𝑠𝑖𝑛 𝛼 2 + 𝑐𝑜𝑠 𝛼 2 𝑐𝑜𝑠 𝛼 2 − 𝑠𝑖𝑛 𝛼 2 𝑐𝑜𝑠 𝛼 2 − 𝑠𝑖𝑛 𝛼 2 = 𝑐𝑜𝑠 ∝ 1 𝑐𝑜𝑠 𝛼 2 + 1 𝑠𝑖𝑛 𝛼 2 𝑐𝑜𝑠 ∝ 𝑠𝑒𝑐 ∝ 2 + 𝑐𝑜𝑠𝑒𝑐 ∝ 2 = 𝑐𝑜𝑠 ∝ 𝑠𝑖𝑛 ∝ 𝑐𝑜𝑠 𝛼 2 − 𝑠𝑖𝑛 𝛼 2 2 𝑐𝑜𝑠 ∝ = 1 2 𝑠𝑖𝑛 ∝ 𝑐𝑜𝑠 𝛼 2 − 𝑠𝑖𝑛 𝛼 2
- 29. 𝒑𝒈 𝟐𝟔𝟏 − 𝟐𝟔𝟐 = 𝑐𝑜𝑠 𝐴 𝑡𝑎𝑛 𝐴 2 1 − 𝑡𝑎𝑛2 𝐴 2 𝑐𝑜𝑠 𝐴 1 𝑡𝑎𝑛 𝐴 2 − 𝑡𝑎𝑛 𝐴 2 = 1 2 𝑐𝑜𝑠 𝐴 𝑡𝑎𝑛 𝐴 𝑠𝑖𝑚𝑖𝑙𝑎𝑟 𝑡𝑜 𝑒𝑥𝑎𝑚𝑝𝑙𝑒 25 = 1 2 𝑠𝑖𝑛 𝐴
Editor's Notes
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- 4. (c) (sin 30) / 2
- https://www.onlinemathlearning.com/half-angle-examples.html
- https://www.onlinemathlearning.com/half-angle-examples.html
- Completed 19-Jun
- https://www.onlinemathlearning.com/half-angle-examples.html
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- http://amsi.org.au/ESA_Senior_Years/SeniorTopic2/2d/2d_3links_3.html
- http://amsi.org.au/ESA_Senior_Years/SeniorTopic2/2d/2d_3links_3.html
- Completed 26-Jun
- https://www.onlinemathlearning.com/half-angle-examples.html
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