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  1. #1
    godzilla2012's Avatar
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    Trigonometric Identities

    You will encounter these in Pre-calculus and have to know these in Calculus.

    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)

    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)

    DOUBLE ANGLE IDENTITIES

    sin2x = 2sinxcosx
    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



    Will add the rest later.

  2. #2
    Dr.Dental's Avatar
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    You usually have a formula sheet for all these... Make sure csc is cosec so ppl understand easier.