Formula

 

Math formula

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)

Trigonometry Table

Sin & Cos values at different angles 

Sin	Cos
Sin 0° = 0	Cos 0° = 1
Sin 30° = 1/2	Cos 30° =  √3/2.
Sin 45° = 1/√2	Cos 45° = 1/√2
Sin 60° = √3/2	Cos 60° = 1/2
Sin 90° = 1	Cos 90 °= 0

Tan and Cot values at different angles

Tan	Cot
Tan 0° = 0	Cot 0° = ∞
Tan 30° = 1/√3	Cot 30° =  √3
Tan 45° = 1	Cot 45° = 1
Tan 60° = √3	Cot 60° = 1√3
Tan 90° = ∞	Cot 90 °= 0

Sec and Cosec values at different angles

Sec	Cosec
Sec 0° = 1	Cosec 0° = 1
Sec 30° = 2/√3	Cosec 30° = 2
Sec 45° = √2	Cosec 45° = √2
Sec 60° = 2	Cosec 60° = 2/√3
Sec 90° = ∞	Cosec 90 °= 1

Trigonometry Formula

» 2ѕinA.coѕB = ѕiη(A + B) + ѕiη(A - B)

» 2cosAѕiηB = ѕiη(A + B) - ѕiη(A - B)

» 2cosA coѕB = coѕ(A + B) + coѕ(A - B)

» 2ѕιηA ѕιηB = coѕ(A - B) - coѕ(A + B)

» ѕιη(A + B) = ѕιηA ¢σѕB + coѕA ѕιηB

» coѕ(A + B) = cosA cosB - sinA sinB

» ѕιη(A - B) = sinA cosB - cosA sinB

» cos(A - B) = cosA cosB + sinA sinB

» тαn(A + B) = (тαnA + тαnB) / (1− тαnA тαnB)

» тαn(A - B) = (тαnA − тαnB) / (1+ тαnA тαnB)

» cot(A + B) = (cotA cotB − 1) / (cotA + cotB)

» cot(A - B) = (cotA cotB + 1) / (¢σтB− ¢σтA)

» ѕιη(A + B) = ѕιηA cosB + cosA ѕιηB

» cos(A + B) = cosA cosB +ѕιnA ѕιηB

» ѕιη(A - B) = ѕιηA cosB - cosA ѕιηB

» ¢σѕ(A - B) = cosA cosB + sinA ѕιηB

» тαη(A + B)= (тαηA + тαηB) / (1 − тαηA тαηB)

» тαη(A − B)= (тαηA − тαηB) / (1+ тαηαтαηв)

» cot(A + B)= (cotA cotB −1) / (cotA + cotB)

» cot(A − B)= (cotA cotB + 1) / (cotA − cotB)

A/ѕιηA = B/ѕιηB = C/ѕιηC = 2я

» A = B cosC + C cosB

» в = A cosC + C cosA

» C = A cosB + B cosA

» cosA = (B² + C² − A²) / 2BC

» cosB = (C² + A² − B²) / 2CA

» cosC = (A² + B²− C²) / 2CA

» Δ = ABC/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

» ѕιη²A + coѕ²A = 1

» ѕec²A - тαη²A=1

» cosec²A + coт²A = 1

» ѕιηA = 1/cosecA

» cosecA = 1/ѕιηA