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Math Help - Proving Trigonometric identity

  1. #1
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    Proving Trigonometric identity

    ((cos^2)x - (sin^2)x) /( (cos ^2)x + SinxCosx) = 1 - tanx

    I simplified the right side to (cosx - sinx) / (cosx)

    Don't know what to do after
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  2. #2
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    convert

    1 - tan x into it's parts

    1 - tan x => 1 - sin x / cos x

    (cos x - sin x) / (cos x) = 1 - sin x / cos x

    multiply each side by cos x

    (cos x) (cos x - sin x) / (cos x) = (cos x) (1 - sin x / cos x)

    (cos x - sin x) = (cos x - sin x)

    You should be able to take it from there.
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  3. #3
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    Hello, Devi09!


    [(cos x)^2 - (sin x)^2] / [(cos x)^2 + (sin x)(cos x)] .= .1 - tan x

    I simplified the right side to: .(cos x - sin x) / (cos x)

    . . . . . . . . . . . . .(cos x)^2 - (sin x)^2 . . . . . (cos x - sin x)(cos x + sin x)
    The left side: . ----------------------------- . = . -------------------------------
    . . . . . . . . . . . (cos x)^2 + (sin x)(cos x) . . . . . . cos x(cos x + sin x)


    . . . . . . cos x - sin x . . . . cos x . . sin x
    Then: . -------------- . = . ------- - ------ . = . 1 - tan x
    . . . . . . . . cos x . . . . . . . cos x . . cos x

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  4. #4
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    Quote Originally Posted by Soroban View Post
    Hello, Devi09!



    . . . . . . . . . . . . .(cos x)^2 - (sin x)^2 . . . . . (cos x - sin x)(cos x + sin x)
    The left side: . ----------------------------- . = . -------------------------------
    . . . . . . . . . . . (cos x)^2 + (sin x)(cos x) . . . . . . cos x(cos x + sin x)


    . . . . . . cos x - sin x . . . . cos x . . sin x
    Then: . -------------- . = . ------- - ------ . = . 1 - tan x
    . . . . . . . . cos x . . . . . . . cos x . . cos x


    For the denominator of the first line how does (cos x)^2 + (sin x)(cos x) become cos x(cos x + sin x) ?

    and for the last line, how does (cos x - sin x)/(cos x) become (cosx / cosx) - (sinx /cosx)
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