Trig Identities

Pythagorean Identity

cos² + sin² = 1

sin² in terms of cos²

sin² = 1 - cos²

cos² in terms of sin²

cos² - 1 = sin²

Relationship between tan and sec

1 + tan² = sec²

Identity involving tangent and secant

tan² - sec² = -1

tan² in terms of sec²

tan² = sec² - 1

Cotangent identity

1 + cot² = csc²

Identity involving cotangent and cosecant

cot² - csc² = -1

cot² in terms of csc²

cot² = csc² - 1

Sum formula for sine

sin(a + b) = sin(a) cos(b) + sin(b) cos(a)

Difference formula for sine

sin(a - b) = sin(a) cos(b) - sin(b) cos(a)

Sum formula for cosine

cos(a + b) = cos(a) cos(b) - sin(a) sin(b)

Difference formula for cosine

cos(a - b) = cos(a) cos(b) + sin(a) sin(b)

Double angle formula for cosine

cos(2x) = cos² - sin²

Another form of cos(2x)

cos(2x) = 2 cos² - 1

Alternative form of cos(2x)

cos(2x) = 1 - 2sin²

Double angle formula for sine

sin(2x) = 2sin cos