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Math Help - Another simple trig identity

  1. #1
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    Another simple trig identity

    This looks simple of paper but for the life of me I can't seem to figure it out

    LS=cos(x-y)cosy-sin(x-y)siny

    RS= cosx

    Greatly appreciated!
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  2. #2
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    Hello, youngb11!

    Do you know your Compound Angle Identities?

    . . \cos(A \pm B) \:=\:\cos A\cos B \mp \sin A\sin b

    . . \sin(A \pm B) \;=\;\sin A\cos B \pm \cos A\sin B


    \cos(x-y)\cos y- \sin(x-y)\sin y\;=\;\cos x

    The left side is:

    . . (\cos x\cos y + \sin x\sin y)\cos y - (\sin x\cos y - \cos x\sin y)\sin y

    . . . . =\; \cos x\cos^2\!y + \underbrace{\sin x\sin y\cos y - \sin x\sin y\cos y}_{\text{These cancel}} + \cos x\sin^2\!y

    . . . . =\;\cos x\cos^2\!y + \cos x\sin^2\!y

    . . . . =\; \cos x\underbrace{(\cos^2\!y + \sin^2\!y)}_{\text{This is 1}}
    . . . . =\; \cos x

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  3. #3
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    Thanks a lot! I can't believe I missed that.

    Thanks again and have a great day!
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