Trigonometry Formula

Trigonometry Formula

The Trigonometric formulas or Identities are the equations which are true in the case of Right-Angled Triangles. Some of the special trigonometric identities are as given below –

1. Pythagorean Identities

  • sin ² θ + cos ² θ = 1
  • tan 2 θ + 1 = sec2 θ
  • cot2 θ + 1 = cosec2 θ
  • sin 2θ = 2 sin θ cos θ
  • cos 2θ = cos² θ – sin² θ
  • tan 2θ = 2 tan θ / (1 – tan² θ)
  • cot 2θ = (cot² θ – 1) / 2 cot θ

2. Sum and Difference identities-

For angles A and B, we have the following relationships:

  • sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
  • cos(A + B) = cos(A)cos(B) – sin(A)sin(B)
  • tan(A + B) = tan(A) + tan(B)/1−tan(A) tan(B)
  • sin(A – B) = sin(A)cos(B) – cos(A)sin(B)
  • cos(A – B) = cos(A)cos(B) + sin(u)sin(v)
  • tan(A – B) = tan(A) − tan(B)/1+tan(A) tan(B)

3. If A, B and C are angles and a, b and c are the sides of a triangle, then,

Sine Laws

  • a/sinA = b/sinB = c/sinC

Cosine Laws

  • c2 = a2 + b2 – 2ab cos C
  • a2 = b2 + c2 – 2bc cos A
  • b2 = a2 + c2 – 2ac cos B

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