Useful Formulas - Arithmetic & Trigonometric Formulaes

Please find some useful formulas as below

--> (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) 

Trigonometric Formulaes

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

🍄🍄🍄🍄🍄

» 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 

Be Confident, Do Confident.

Cheers!!