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