TRIGONOMETRIC IDENTITIES

BASIC TRIG IDENTITIES

Pythagorean

sin²x + cos²x = 1

1 + tan²x = sec²x

1 + cot²x = csc²x

Reciprocal

sin x =

• 1/csc x

cos x =

• 1/sec x

tan x =

• 1/cot x

csc x =

• 1/sin x

sec x =

• 1/cos x

cot x =

• 1/tan x

Co-function

sin π/2 - x =

• cos x

cos π/2 - x =

• sin x

tan π/2 - x =

• cot x

cot π/2 -x =

• tan x

sec π/2 - x =

• csc x

csc π/2 - x =

• sec x

Even-odd

sin (-x) = -sinx

cos (-x) = cos x

tan (-x) = -tanx

sec (-x) = sec x

cot (-x) = -cotx

csc (-x) = -cscx

Double-angle

sin 2x =

• 2sin x cos x

cos 2x =

• cos²x - sin²x

• 2cos²x - 1

• 1 - 2sin²x

tan 2x =

• 2tanx/1-tan²x

DERIVATIVES

d/dx sin x =

• cos x

d/dx cos x =

• -sinx

d/dx tan x =

• sec²x

d/dx cot x =

• -csc²x

d/dx sec x =

• sec x tan x

d/dx csc x =

-csc x cot x

INTEGRALS

∫ sin x dx =

• -cos x + C

∫ cos x dx =

• sin x + C

∫ tan x dx =

• ln (sec x) + C

∫ cot x dx =

• ln (sin x) + C

∫ sec x dx =

• ln (sec x + tan x) +C

∫ csc x dx =

• ln (csc x - cot x) + C

POWER REDUCING IDENTITY

sin²x =

• 1 - cos 2x/2

cos²x =

• 1 + cos 2x/2

tan²x =

• 1 - cos 2x/1 + cos 2x

TANGENT AND COTANGENT

tan x =

• sin x/cos x

cot x =

• cos x/sin x