MATHEMATICAL FORMULA HANDBOOK

Hyperbolic Function Diffrentiation Algebra

• Trigonometric Function

1. cos²A + sin²A = 1
2. sec²A - tan²A =1
3. cosec²A - cot²A = 1
4. sin2A = 2sinAcosA
5. cos2A = cos²A - cot²A = 1
6. tan2A = (2tanA) ⁄ (1 - tan²A)
7. sin(A±B) = sinAcosB±cosAsinB
8. cos(A±B) = cosAcosB±sinAsinB
9. tan(A±B) = tan(A±B) ⁄ 1-tanAtanB
10. cosAcosB = cos(A+B) + cos(A-B) ⁄ 2
11. sinAsinB = cos(A-B) - cos(A+B) ⁄ 2
12. sinAcosB = sin(A+B) + sin(A-B) ⁄ 2
13. sinA + sinB = 2 sin(A+B ⁄ 2) cos(A-B ⁄ 2)
14. sinA - sinB = 2 cos(A+B ⁄ 2) sin(A-B ⁄ 2)
15. cosA + cosB = 2 cos(A+B ⁄ 2) cos(A-B ⁄ 2)
16. cosA - cosB = -2 sin(A+B ⁄ 2) sin(A-B ⁄ 2)

Relations between sides and angles of any plane triangle

In a plane triangle with angles A,B, and C and sides opposite a,b, and c respectively,

a ⁄ sinA = b ⁄ sinB = c ⁄ sinC = diameter of circumscribed circle.

a² = b² + c² - 2bc cosA

a = b cosC + c cosB

cosA = (b² + c² − a²) ⁄ 2bc

tan(A-B ⁄ 2) = (a-b) ⁄ (a+b) cot C ⁄ 2

area = ½ ab sinC = ½ bc sinA = ½ ca sinB = √ s(s-a)(s-b)(s-c) , where s=½ (a+b+c)

Relations between sides and angles of any spherical triangle

In a spherical triangle with angles A,B, and C and sides opposite a,b, and c respectively,

sina ⁄ sinA = sinb ⁄ sinB = sinc ⁄ sinC

cosa = cos b cos c + sin b sin c cos A

cosA = -cos B cos C + sinB sin C cos a

THANK YOU