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January 1st, 2017, 06:49 AM   #1
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trigonometric identities

given 5e^x - 4e^-x ≡A sinh x + B cosh x

Find A and B
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January 1st, 2017, 07:16 AM   #2
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given 5e^x - 4e^-x ≡A sinh x + B cosh x

Find A and B
$5e^x-4e^{-x} = \dfrac{A(e^x - e^{-x})}{2} + \dfrac{B(e^x + e^{-x})}{2}$

$5e^x-4e^{-x} = \dfrac{(A+B)e^x + (B-A)e^{-x}}{2}$

$10e^x-8e^{-x} = (A+B)e^x + (B-A)e^{-x}$

$A+B = 10$

$B-A = -8$

can you finish?
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January 1st, 2017, 05:42 PM   #3
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$$5e^x-4e^{-x}=8\sinh x+e^x=8\sinh x+ \sinh x+\cosh x=9\sinh x+\cosh x$$
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January 4th, 2017, 02:56 PM   #4
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Originally Posted by skeeter View Post
$5e^x-4e^{-x} = \dfrac{A(e^x - e^{-x})}{2} + \dfrac{B(e^x + e^{-x})}{2}$

$5e^x-4e^{-x} = \dfrac{(A+B)e^x + (B-A)e^{-x}}{2}$

$10e^x-8e^{-x} = (A+B)e^x + (B-A)e^{-x}$

$A+B = 10$

$B-A = -8$

can you finish?
unfortunately not, more studying required on this topic i think
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January 4th, 2017, 03:00 PM   #5
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unfortunately not, more studying required on this topic i think
come on ... it's basic algebra for solving a system of equations.

adding the last two equations term for term eliminates $A$ and yields the equation

$2B=2$

find $B$ and $A$ now?
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January 4th, 2017, 03:44 PM   #6
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Originally Posted by skeeter View Post
come on ... it's basic algebra for solving a system of equations.

adding the last two equations term for term eliminates $A$ and yields the equation

$2B=2$

find $B$ and $A$ now?

of course, i couldnt see the wood for the trees in that instance i had got myself so confused in the other questions i am doing, i had the answer for this one a long time ago, your method and stages really helped me so thank you
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