Can you please prove sinh(2x)= 2 sinh(x) cos(x)?

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Can you please prove sinh(2x)= 2 sinh(x) cos(x)?

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Answer 1 · 2018-05-12T16:01:10

$R . H . S = 2 sinh (x) cosh (x) = 2 \cdot [\frac{e^{x} - e^{- x}}{2}] \cdot [\frac{e^{x} + e^{- x}}{2}] =$ $R.H.S=2 sinh(x) cosh(x)=2*[(e^x-e^-x)/2]*[(e^x+e^-x)/2]=$

$[\frac{e^{2 x} + 1 - 1 - e^{- 2 x}}{2}] = \frac{e^{2 x} - e^{- 2 x}}{2} = sinh (2 x) = L . H . S$ $[(e^(2x)+1-1-e^(-2x))/2]=[e^(2x)-e^(-2x)]/2=sinh(2x)=L.H.S$

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$sinh (2 x) = 2 sinh (x) cosh (x)$ $sinh(2x)=2 sinh(x) cosh(x)$

$R . H . S = 2 sinh (x) cosh (x) = 2 \cdot [\frac{e^{x} - e^{- x}}{2}] \cdot [\frac{e^{x} + e^{- x}}{2}] =$ $R.H.S=2 sinh(x) cosh(x)=2*[(e^x-e^-x)/2]*[(e^x+e^-x)/2]=$

$[\frac{e^{2 x} + 1 - 1 - e^{- 2 x}}{2}] = \frac{e^{2 x} - e^{- 2 x}}{2} = sinh (2 x) = L . H . S$ $[(e^(2x)+1-1-e^(-2x))/2]=[e^(2x)-e^(-2x)]/2=sinh(2x)=L.H.S$

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Can you please prove sinh(2x)= 2 sinh(x) cos(x)?

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