Mathematics all important formalae

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(α+в+¢)²= α²+в²+¢²+2(αв+в¢+¢α)
1. (α+в)²= α²+2αв+в²
2. (α+в)²= (α-в)²+4αв b
3. (α-в)²= α²-2αв+в²
4. (α-в)²= f(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

 1. ѕιη2α = 2ѕιηα¢σѕα

2. ¢σѕ2α = ¢σѕ²α − ѕιη²α

3. ¢σѕ2α = 2¢σѕ²α − 1

4. ¢σѕ2α = 1 − ѕιη²α

5. 2ѕιη²α = 1 − ¢σѕ2α

6. 1 + ѕιη2α = (ѕιηα + ¢σѕα)²

7. 1 − ѕιη2α = (ѕιηα − ¢σѕα)²

8. тαη2α = 2тαηα / (1 − тαη²α)

9. ѕιη2α = 2тαηα / (1 + тαη²α)

10. ¢σѕ2α = (1 − тαη²α) / (1 + тαη²α)

11. 4ѕιη³α = 3ѕιηα − ѕιη3α

12. 4¢σѕ³α = 3¢σѕα + ¢σѕ3α