Important Formulas for Everyone

9th,10th,11th,12th,
important formula's  which is Very usefully

Hi Friend's
Today, we are telling you some math formula's which are important for children's and for Elders also

many times When we do not have a book, but we need some formula's to solve some math problems then we check formula's in different places.
But not all get the same place, so today we will try to do the same thing a little easier

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Some basic formula's which is everybody should know

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)

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some advanvance formula's

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

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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

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» 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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thank you Friend's 
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