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Math Help - verify the identity

  1. #1
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    verify the identity

    sinh(x+y) = sinh(x)cosh(y) + cosh(x)sinh(y)

    im not sure how to verify this, i suppose i would try to plug numbers into the equation and solve both sides. i suppose im looking for a more efficient way to verify this without having to plug and chug. thanks in advance
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  2. #2
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    Dear slapmaxwell1,

    By definition, Sinh(x+y)=\frac{e^{x+y}-e^{-x-y}}{2}

    SinhxCoshy+CoshxSinhy=\frac{(e^x-e^{-x})(e^y+e^{-y})}{4}+\frac{(e^y-e^{-y})(e^x+e^{-x})}{4}

    By simplification, SinhxCoshy+CoshxSinhy=\frac{e^{x+y}-e^{-x-y}}{2}

    Therefore, sinh(x+y) = sinh(x)cosh(y) + cosh(x)sinh(y)

    Hope this helps.
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