Trigonometric Identities

cscθ

1/sinθ (Reciprocal Identity)

sinθ

1/cscθ (Reciprocal Identity)

secθ

1/cosθ (Reciprocal Identity)

cosθ

1/secθ (Reciprocal Identity)

cotθ

1/tanθ (Reciprocal Identity)

tanθ

1/cotθ (Reciprocal Identity)

tan θ

sinθ/cosθ (Quotient Identity)

cot θ

cosθ/sinθ (Quotient Identity)

sin²θ + cos²θ

1 (Pythagorean Identity)

tan²θ + 1

sec²θ (Pythagorean Identity)

1 + cot²θ

csc²θ (Pythagorean Identity)

sin(α ± β)

sinαcosβ ± sinβcosα (Sum and Difference Identities)

cos(α ± β)

cosαcosβ ∓ sinαsinβ (Sum and Difference Identities)

tan(α ± β)

tan α ± tan β / 1 ∓ tan α tan β (Sum and Difference Identities)

sin 2θ

2sinθcosθ (Double Angle Identities)

tan 2θ

2 tanθ / 1 − tan²θ (Double Angle Identites)

cos 2θ

cos²θ-sin²θ (Double Angle Identites)

cos 2θ

2cos²θ-1 (Double Angle Identites)

cos 2θ

1-2sinθ (Double Angle Identites)