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Algebric identities

(a + b)2 = a2 + b2 + 2ab
(a + b)2 = (a-b)2 + 4ab
(a - b)2 = a2 + b2 - 2ab
(a - b)2 = (a+b)2 - 4ab
(a + b)3 = a3 + b3 + 3a2b + 3ab2
(a + b)3 = a3 + b3 + 3ab(a + b)
(a - b)3 = a3 - b3 - 3a2b + 3ab2
(a - b)3 = a3 - b3 - 3ab(a - b)
a2 - b 2 = (a + b)(a - b)
a2 + b 2 = (a + b)2 - 2ab = (a - b)2 + 2ab
(a + b)2 + (a - b)2 = 2(a2 + b2)
a3 - b3 = (a - b)(a2+ ab + b2)
a3 - b3 =(a - b)3+3ab(a - b)
a3 + b3 = (a + b)(a2- ab + b2)
a3 + b3 = (a + b)3-3ab(a + b)
a3 + b3 + c3 -3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

cross multiplication method

trigonometric identities

sin2θ + cos2θ = 1
sin2θ = 1 - cos2θ
cos2θ = 1 - sin2θ
sec2θ - tan2θ = 1
sec2θ = 1 + tan2θ
tan2θ = sec2θ - 1
cosec2θ - cot2θ = 1
cosec2θ = 1 + cot2θ
cot2θ = cosec2θ - 1
tan θ = sinθ / cos θ
cot θ = cos θ / sin θ

  • sin(A + B) = sinA*cosB + cosA*sinB
  • sin(A - B) = sinA*cosB - cosA*sinB
  • cos(A + B) = cosA*cosB - sinA*sinB
  • cos(A - B) = cosA*cosB + sinA*sinB
  • sin(A + B)*sin(A - B) = sin2A - sin2B = cos2B - cos2A
  • cos(A + B)*cos(A - B) = cos2A - sin2B = cos2B - sin2A
  • 2sinAcosB = sin(A + B) + sin(A - B)
  • 2cosAsinB= sin(A + B) - sin(A - B)
  • 2cosAcosB = cos(A + B) + cos(A - B)
  • 2sinAsinB = cos(A - B) - cos(A + B)
  • sin2A = 2sinAcosA = 2tanA/(1 + tan2A)
  • cos2A = cos2A - sin2A = 1 - 2sin2A = 2cos2A - 1 = (1 - tan2A)/(1 + tan2A)
  • tan2A = 2tanA/(1 - tan2A)
  • 2sin2A = 1 - cos2A
  • 2cos2A = 1 + cos2A
  • sin3A = 3sinA - 4sin3A
  • cos3A = 4cos3A - 3cosA
  • tan3A = (3tanA - tan3A)/(1 - 3tan2A)

co-ordinate geometry formulas

distance between two points co-ordinates of point which devides line segments in the ratio m by n