#Foydali

Qisqa ko'paytirish formulalari

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)

Trigonometrik formulalar

☘️ ѕιη0° =0
☘️ ѕιη30° = 1/2
☘️ ѕιη45° = 1/√2
☘️ ѕιη60° = √3/2
☘️ ѕιη90° = 1
☘️ тαη0° = 0
☘️ тαη30° = 1/√3
☘️ тαη45° = 1
☘️ тαη60° = √3
☘️ тαη90° = ∞
☘️ ѕє¢0° = 1
☘️ ѕє¢30° = 2/√3
☘️ ѕє¢45° = √2
☘️ ѕє¢60° = 2
☘️ ѕє¢90° = ∞


🔹 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

🔻 ѕιη2α = 2ѕιηα¢σѕα
🔻 ¢σѕ2α = ¢σѕ²α − ѕιη²α
🔻 ¢σѕ2α = 2¢σѕ²α − 1
🔻 ¢σѕ2α = 1 − ѕιη²α
🔻 2ѕιη²α = 1 − ¢σѕ2α
🔻 1 + ѕιη2α = (ѕιηα + ¢σѕα)²
🔻 1 − ѕιη2α = (ѕιηα − ¢σѕα)²
🔻 тαη2α = 2тαηα / (1 − тαη²α)
🔻 ѕιη2α = 2тαηα / (1 + тαη²α)
🔻 ¢σѕ2α = (1 − тαη²α) / (1 + тαη²α)
🔻 4ѕιη³α = 3ѕιηα − ѕιη3α
🔻 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

@matematika_ustozi