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If $$\ \tanh x=\dfrac {2}{3}$$ . Find the value of x and then cosh 2x.

written 3.9 years ago by teamques10 ★ 69k

modified 2.3 years ago by sagarkolekar ★ 11k

engineering mathematics

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written 3.9 years ago by teamques10 ★ 69k

$\tanh x = \dfrac{(e^x-e^{-x})}{(e^x+e^{-x})}$ Let $a=e^x$ $b=\dfrac {1}{e^x }$ $\therefore \tanh x = \dfrac{a-b}{a+b}$ $\dfrac23 = \dfrac{a-b}{a+b}$ $2a+2b=3a-3b$ $a=5b$ $\dfrac ab=e^{2x}$ $2x=\log(a/b)$ $\therefore x=0.5\log(5)$ $\therefore \cosh 2x=\cosh(\log5)$ $\therefore \cosh 2x=2.6$

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