Trigonometry Identities, Trigonometry Identities, Trig Identities

1 + tan² θ

cot² θ + 1

tan θ

sin²θ+cos²θ=?

1

cos(a-b)

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

cos(a+b)

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

sin(a+b)

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

sin(a-b)

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

sin(2θ)=

2sinθcosθ

cos(2θ)=

cos²θ-sin²θ

sin(x/2)

cos(x/2)

tan(x/2)

sin²x

Power Reducing identity

cos²x

Power Reducing identity

tan²x

Power Reducing identity

sin²(x) (Pythagorean Identity)

1 - cos²x

cos²(x) (Pythagorean Identity)

1 - sin²x

tan²(x) (Pythagorean Identity)

sec²x - 1

sec²(x) (Pythagorean Identity)

tan²x + 1

cot²(x) (Pythagorean Identity)

csc²x - 1

csc²(x) (Pythagorean Identity)

1 + cot²x

tan(a + b)

sin x (Reciprocal Identity)

1/(csc x)

cos x (Reciprocal Identity)

1/(sec x)

tan x (Reciprocal Identity)

1/(cot x)

tan 30° or tan π/6

tan 45° or tan π/4

1

tan 60° or tan π/3

tan 90° or tan π/2

Undefined

tan 180° or π

0

Quadrants where sin x is positive

Quadrant I and II

Quadrant where sin x is positive and tan x is negative

Quadrant II

Quadrant where tan x is positive and cos x is negative

Quadrant III