If sinh3x-cosh3x-kex-ekx1-k then k-

The correct option is C 3 As we know that #160; (a b)^3 (a+b)^3= 3 a^2 b b^3 As sinh x=e^x e^ x2,cosh x=e^x+e^ x2 sinh^3 x cosh ^3 x=(e^x ...

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Standard XII

Mathematics

General Solution of Trigonometric Equation

If sinh3x-c...

Question

If ${sinh}^{3} x - {cosh}^{3} x = \frac{k e^{x} - e^{k x}}{1 - k}$ then $k =$

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Solution

The correct option is C $- 3$
As we know that
$(a - b)^{3} - (a + b)^{3} = - 3 a^{2} b - b^{3}$
As $sinh x = \frac{e^{x} - e^{- x}}{2}, cosh x = \frac{e^{x} + e^{- x}}{2}$
${sinh}^{3} x - {cosh}^{3} x = \frac{(e^{x} - e^{- x})^{3} - (e^{x} + e^{- x})^{3}}{2^{3}}$
$= \frac{- 3 e^{2 x} \times e^{- x} - e^{- 3 x}}{8} = \frac{- 3 e^{x} - e^{- 3 x}}{2 (1 - (- 3))}$
So $k = - 3$

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If sinh3x−cosh3x=kex−ekx1−k then k=

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