Here we have mentioned 9th,10th,11th,12th Mathematics formula.

(α+в+¢)⊃2;= α⊃2;+в⊃2;+¢⊃2;+2(αв+в¢+¢α)

1. (α+в)⊃2;= α⊃2;+2αв+в⊃2;

2. (α+в)⊃2;= (α-в)⊃2;+4αв b

3. (α-в)⊃2;= α⊃2;-2αв+в⊃2;

4. (α-в)⊃2;= f(α+в)⊃2;-4αв

5. α⊃2; + в⊃2;= (α+в)⊃2; – 2αв.

6. α⊃2; + в⊃2;= (α-в)⊃2; + 2αв.

7. α⊃2;-в⊃2; =(α + в)(α – в)

8. 2(α⊃2; + в⊃2;) = (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;=α⊃2;+в⊃2; + ¢⊃2; +2(αв + в¢ + ¢α)

12. (α + в)⊃3; = α⊃3; + 3α⊃2;в + 3αв⊃2; + в⊃3;

13. (α + в)⊃3; = α⊃3; + в⊃3; + 3αв(α + в)

14. (α-в)⊃3;=α⊃3;-3α⊃2;в+3αв⊃2;-в⊃3;

15. α⊃3; + в⊃3; = (α + в) (α⊃2; -αв + в⊃2;)

16. α⊃3; + в⊃3; = (α+ в)⊃3; -3αв(α+ в)

17. α⊃3; -в⊃3; = (α -в) (α⊃2; + αв + в⊃2;)

18. α⊃3; -в⊃3; = (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 = (в⊃2; + ¢⊃2;− α⊃2;) / 2в¢

» ¢σѕв = (¢⊃2; + α⊃2;− в⊃2;) / 2¢α

» ¢σѕ¢ = (α⊃2; + в⊃2;− ¢⊃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 = ¢σѕ⊃2;α − ѕιη⊃2;α

3. ¢σѕ2α = 2¢σѕ⊃2;α − 1

4. ¢σѕ2α = 1 − ѕιη⊃2;α

5. 2ѕιη⊃2;α = 1 − ¢σѕ2α

6. 1 + ѕιη2α = (ѕιηα + ¢σѕα)⊃2;

7. 1 − ѕιη2α = (ѕιηα − ¢σѕα)⊃2;

8. тαη2α = 2тαηα / (1 − тαη⊃2;α)

9. ѕιη2α = 2тαηα / (1 + тαη⊃2;α)

10. ¢σѕ2α = (1 − тαη⊃2;α) / (1 + тαη⊃2;α)

11. 4ѕιη⊃3;α = 3ѕιηα − ѕιη3α

12. 4¢σѕ⊃3;α = 3¢σѕα + ¢σѕ3α

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» ѕιη⊃2;Θ+¢σѕ⊃2;Θ=1

» ѕє¢⊃2;Θ-тαη⊃2;Θ=1

» ¢σѕє¢⊃2;Θ-¢σт⊃2;Θ=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