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Math Help - Verify Trig Identities:Simplify W/Picture

  1. #1
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    Verify Trig Identities:Simplify W/Picture

    Just simplify. See picture that is attaches. I know the even odd properties I know sin(-x) is -sinx. After that I got stuck. I tried to multiply by conjugate didnt work.
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  2. #2
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    Re: Verify Trig Identities:Simplify W/Picture

    The answer is sin(x). So you have sin^2(-x)- sin(-x) / 1 - sin(-x) . sin^2(-x) is really just sin(-x) * sin(-x), which becomes -1*-1*sin(x)*sin(x) = sin^2 (x). So you have sin^2 (x) - sin(x) / sin(x) + 1. Take out the sin(x) on the top and you have
    (sin(x)( sin(x) + 1)) / (sin(x) + 1). Cancel out the (sin(x)+1) and you have sin(x) left.
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  3. #3
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    Re: Verify Trig Identities:Simplify W/Picture

    Any advice for verifying trig identities?
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  4. #4
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    Re: Verify Trig Identities:Simplify W/Picture

    Its kinda hard wo read that Shadow can you do it on paint and upload picture?
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  5. #5
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    Re: Verify Trig Identities:Simplify W/Picture

    View: j5bwY4.png - cubeupload

    Does that make sense?
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  6. #6
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    Re: Verify Trig Identities:Simplify W/Picture

    Hello, ShadowKnight8702!

    Your work is correct.


    \frac{\sin^2(\text{-}x) - \sin(\text{-}x)}{1-\sin(\text{-}x)}

    . . . =\;\frac{[\sin(\text{-}x)][\sin(\text{-}x)] - (\text{-}\sin x)}{1 - (\text{-}\sin x)}

    . . . =\;\frac{(\text{-}\sin x)(\text{-}\sin x) + \sin x}{1 + \sin x}

    . . . =\;\frac{\sin^2\!x + \sin x}{1 + \sin x}

    . . . =\;\frac{\sin x({\color{red}\rlap{////////}}\sin x + 1)}{{\color{red}\rlap{///////}}1 + \sin x}

    . . . =\;\sin x

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  7. #7
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    Re: Verify Trig Identities:Simplify W/Picture

    I got it thanks for your help both of you.
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