Maths formulas improved ur knowledge

in #study5 years ago

Enhance your knowledge.

  1. (α+в)²= α²+2αв+в²
  2. (α+в)²= (α-в)²+4αв
  3. (α-в)²= α²-2αв+в²
  4. (α-в)²= (α+в)²-4αв
  5. α² + в²= (α+в)² - 2αв.
  6. α² + в²= (α-в)² + 2αв.
  7. α²-в² =(α + в)(α - в)
  8. 2(α² + в²) = (α+ в)² + (α - в)²
  9. 4αв = (α + в)² -(α-в)²
  10. αв ={(α+в)/2}²-{(α-в)/2}²
  11. (α + в + ¢)² = α² + в² + ¢² + 2(αв + в¢ + ¢α)
  12. (α + в)³ = α³ + 3α²в + 3αв² + в³
  13. (α + в)³ = α³ + в³ + 3αв(α + в)
  14. (α-в)³=α³-3α²в+3αв²-в³
  15. α³ + в³ = (α + в) (α² -αв + в²)
  16. α³ + в³ = (α+ в)³ -3αв(α+ в)
  17. α³ -в³ = (α -в) (α² + αв + в²)
  18. α³ -в³ = (α-в)³ + 3αв(α-в)
    ѕιη0° =0
    ѕιη30° = 1/2
    ѕιη45° = 1/√2
    ѕιη60° = √3/2
    ѕιη90° = 1
    ¢σѕ ιѕ σρρσѕιтє σƒ ѕιη
    тαη0° = 0
    тαη30° = 1/√3
    тαη45° = 1
    тαη60° = √3
    тαη90° = ∞
    ¢σт ιѕ σρρσѕιтє σƒ тαη
    ѕє¢0° = 1
    ѕє¢30° = 2/√3
    ѕє¢45° = √2
    ѕє¢60° = 2
    ѕє¢90° = ∞
    ¢σѕє¢ ιѕ σρρσѕιтє σƒ ѕє¢
    2ѕιηα¢σѕв=ѕιη(α+в)+ѕιη(α-в)
    2¢σѕαѕιηв=ѕιη(α+в)-ѕιη(α-в)
    2¢σѕα¢σѕв=¢σѕ(α+в)+¢σѕ(α-в)
    2ѕιηαѕιηв=¢σѕ(α-в)-¢σѕ(α+в)
    ѕιη(α+в)=ѕιηα ¢σѕв+ ¢σѕα ѕιηв.
    » ¢σѕ(α+в)=¢σѕα ¢σѕв - ѕιηα ѕιηв.
    » ѕιη(α-в)=ѕιηα¢σѕв-¢σѕαѕιηв.
    » ¢σѕ(α-в)=¢σѕα¢σѕв+ѕιηαѕιηв.
    » тαη(α+в)= (тαηα + тαηв)/ (1−тαηαтαηв)
    » тαη(α−в)= (тαηα − тαηв) / (1+ тαηαтαηв)
    » ¢σт(α+в)= (¢σтα¢σтв −1) / (¢σтα + ¢σтв)
    » ¢σт(α−в)= (¢σтα¢σтв + 1) / (¢σтв− ¢σтα)
    » ѕιη(α+в)=ѕιηα ¢σѕв+ ¢σѕα ѕιηв.
    » ¢σѕ(α+в)=¢σѕα ¢σѕв +ѕιηα ѕιηв.
    » ѕιη(α-в)=ѕιηα¢σѕв-¢σѕαѕιηв.
    » ¢σѕ(α-в)=¢σѕα¢σѕв+ѕιηαѕιηв.
    » тαη(α+в)= (тαηα + тαηв)/ (1−тαηαтαηв)
    » тαη(α−в)= (тαηα − тαηв) / (1+ тαηαтαηв)
    » ¢σт(α+в)= (¢σтα¢σтв −1) / (¢σтα + ¢σтв)
    » ¢σт(α−в)= (¢σтα¢σтв + 1) / (¢σтв− ¢σтα)
    α/ѕιηα = в/ѕιηв = ¢/ѕιη¢ = 2я
    » α = в ¢σѕ¢ + ¢ ¢σѕв
    » в = α ¢σѕ¢ + ¢ ¢σѕα
    » ¢ = α ¢σѕв + в ¢σѕα
    » ¢σѕα = (в² + ¢²− α²) / 2в¢
    » ¢σѕв = (¢² + α²− в²) / 2¢α
    » ¢σѕ¢ = (α² + в²− ¢²) / 2¢α
    » Δ = αв¢/4я
    » ѕιηΘ = 0 тнєη,Θ = ηΠ
    » ѕιηΘ = 1 тнєη,Θ = (4η + 1)Π/2
    » ѕιηΘ =−1 тнєη,Θ = (4η− 1)Π/2
    » ѕιηΘ = ѕιηα тнєη,Θ = ηΠ (−1)^ηα
  19. ѕιη2α = 2ѕιηα¢σѕα
  20. ¢σѕ2α = ¢σѕ²α − ѕιη²α
  21. ¢σѕ2α = 2¢σѕ²α − 1
  22. ¢σѕ2α = 1 − ѕιη²α
  23. 2ѕιη²α = 1 − ¢σѕ2α
  24. 1 + ѕιη2α = (ѕιηα + ¢σѕα)²
  25. 1 − ѕιη2α = (ѕιηα − ¢σѕα)²
  26. тαη2α = 2тαηα / (1 − тαη²α)
  27. ѕιη2α = 2тαηα / (1 + тαη²α)
  28. ¢σѕ2α = (1 − тαη²α) / (1 + тαη²α)
  29. 4ѕιη³α = 3ѕιηα − ѕιη3α
  30. 4¢σѕ³α = 3¢σѕα + ¢σѕ3α
    » ѕιη²Θ+¢σѕ²Θ=1
    » ѕє¢²Θ-тαη²Θ=1
    » ¢σѕє¢²Θ-¢σт²Θ=1
    » ѕιηΘ=1/¢σѕє¢Θ
    » ¢σѕє¢Θ=1/ѕιηΘ
    » ¢σѕΘ=1/ѕє¢Θ
    » ѕє¢Θ=1/¢σѕΘ
    » тαηΘ=1/¢σтΘ
    » ¢σтΘ=1/тαηΘ
    » тαηΘ=ѕιηΘ/¢σѕΘ
    "..
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