Trigonometric Identities
You will encounter these in Pre-calculus and have to know these in Calculus.
Will add the rest later.
BASIC IDENTITIES
- 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
- sin (-x) = -sin x
- cos(-x) = cos x
- tan (-x) = tan x
- tan x = sin x/cos x
- cot x = sin x/cos x
PYTHAGOREAN IDENTITIES
sin^2 (x) + cos^2 (x) = 1
1 + cot^2 (x) = csc^2 (x)
1 + tan^2 (x) = sec^2 (x)
1 + cot^2 (x) = csc^2 (x)
1 + tan^2 (x) = sec^2 (x)
SUM AND DIFFERENCE IDENTITIES
sin (u + v) = sin u cos v + cos u sin v
sin (u - v) = sin u cos v - cos u sin v
cos (u + v) = cos u cos v - sin u sin v
cos (u - v) = cos u cos v + sin u sin v
tan (u + v) = (tan u + tan v)/(1 - tan u tan v)
tan (u - v) = (tan u - tan v)/(1 + tan u tan v)
sin (u - v) = sin u cos v - cos u sin v
cos (u + v) = cos u cos v - sin u sin v
cos (u - v) = cos u cos v + sin u sin v
tan (u + v) = (tan u + tan v)/(1 - tan u tan v)
tan (u - v) = (tan u - tan v)/(1 + tan u tan v)
DOUBLE ANGLE IDENTITIES
sin2x = 2sinxcosx
cos2x = cos^2x - sin^2x
= 1 - 2sin^2x
= 2cos^2x - 1
tan2x = 2tanx/1 - tan^2x
cos2x = cos^2x - sin^2x
= 1 - 2sin^2x
= 2cos^2x - 1
tan2x = 2tanx/1 - tan^2x
HALF ANGLE IDENTITIES
sin x/2 = (+-)root[(1-cosx)/2]
cos x/2 = (+-)root[(1+cosx)/2]
tan x/2 = (+-)root[(1-cosx)/1+cosx)]
= sinx/1+cosx
= 1-cosx/sinx
cos x/2 = (+-)root[(1+cosx)/2]
tan x/2 = (+-)root[(1-cosx)/1+cosx)]
= sinx/1+cosx
= 1-cosx/sinx
Will add the rest later.