Mathematics Formulas (गणित के सूत्र)

***कुछ महत्वपूर्ण गणित के सूत्र ***

»»»Algebra Related«««

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)
19) (α+в+¢)²= α²+в²+¢²+2(αв+в¢+¢α)

»»»Trigonometri Related««»

1) ѕιη0° =0
2) ѕιη30° = 1/2
3) ѕιη45° = 1/√2
4) ѕιη60° = √3/2
5) ѕιη90° = 1
6) ¢σѕec ιѕ σρρσѕιтє σƒ ѕιη
7) тαη0° = 0
8) тαη30° = 1/√3
9) тαη45° = 1
10) тαη60° = √3
11) тαη90° = ∞
12) ¢σт ιѕ σρρσѕιтє σƒ тαη
13) ѕє¢0° = 1
14) ѕє¢30° = 2/√3
15) ѕє¢45° = √2
16) ѕє¢60° = 2
17) ѕє¢90° = ∞
18) ѕє¢ ιѕ σρρσѕιтє σƒ ¢os

19) 2ѕιηα¢σѕв=ѕιη(α+в)+ѕιη(α-в)
20) 2¢σѕαѕιηв=ѕιη(α+в)-ѕιη(α-в)
21) 2¢σѕα¢σѕв=¢σѕ(α+в)+¢σѕ(α-в)
22) 2ѕιηαѕιηв=¢σѕ(α-в)-¢σѕ(α+в)
23) ѕιη(α+в)=ѕιηα ¢σѕв+ ¢σѕα ѕιηв.
24) ¢σѕ(α+в)=¢σѕα ¢σѕв – ѕιηα ѕιηв.
25) ѕιη(α-в)=ѕιηα¢σѕв-¢σѕαѕιηв.
26)¢σѕ(α+в)=¢σѕα¢σѕв+ѕιηαѕιηв

27) тαη(α+в)= (тαηα + тαηв)/
(1−тαηαтαηв)
28) тαη(α−в)= (тαηα − тαηв) / (1+тαηαтαηв)
29) ¢σт(α+в)= (¢σтα¢σтв −1) / (¢σтα + ¢σтв)
30) ¢σт(α−в)= (¢σтα¢σтв + 1) / (¢σтв− ¢σтα)

31) ѕιη(α+в)=ѕιηα ¢σѕв+ ¢σѕα ѕιηв.
32) ¢σѕ(α+в)=¢σѕα ¢σѕв +ѕιηα ѕιηв.
33) ѕιη(α-в)=ѕιηα¢σѕв-¢σѕαѕιηв.
34)¢σѕ(α_в)=¢σѕα¢σѕв+ѕιηαѕιηв.

35) тαη(α+в)= (тαηα + тαηв)/
(1−тαηαтαηв)
36) тαη(α−в)= (тαηα − тαηв) / (1+
тαηαтαηв)
37) ¢σт(α+в)= (¢σтα¢σтв −1) / (¢σтα + ¢σтв)
38) ¢σт(α−в)= (¢σтα¢σтв + 1) / (¢σтв− ¢σтα)

39) α/ѕιηα = в/ѕιηв = ¢/ѕιη¢ = 2я
» α = в ¢σѕ¢ + ¢ ¢σѕв
» в = α ¢σѕ¢ + ¢ ¢σѕα
» ¢ = α ¢σѕв + в ¢σѕα

40) ¢σѕα = (в² + ¢²− α²) / 2в¢
41) ¢σѕв = (¢² + α²− в²) / 2¢α
42) ¢σѕ¢ = (α² + в²− ¢²) / 2¢α

43) 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

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