If frac{5 sinh 2x}{7+6 cosh 2x} = frac{3}{2}, | vedclass

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(C) Given $\frac{5 \sinh 2x}{7+6 \cosh 2x} = \frac{3}{2}$.Using the identities $\sinh 2x = 2 \sinh x \cosh x$ and $\cosh 2x = 2 \cosh^2 x - 1$,we get:

Vedclass · Accepted Answer

$39$

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(C) Given $\frac{5 \sinh 2x}{7+6 \cosh 2x} = \frac{3}{2}$.Using the identities $\sinh 2x = 2 \sinh x \cosh x$ and $\cosh 2x = 2 \cosh^2 x - 1$,we get:$\frac{5(2 \sinh x \cosh x)}{7+6(2 \cosh^2 x - 1)} = \frac{3}{2}$$\frac{10 \sinh x \cosh x}{12 \cosh^2 x + 1} = \frac{3}{2}$Divide the numerator and denominator by $\cosh^2 x$:$\frac{10 	anh x}{12 + 	ext{sech}^2 x} = \frac{3}{2}$Since $	ext{sech}^2 x = 1 - 	anh^2 x$:$\frac{10 	anh x}{12 + 1 - 	anh^2 x} = \frac{3}{2}$$\frac{10 	anh x}{13 - 	anh^2 x} = \frac{3}{2}$$20 	anh x = 39 - 3 	anh^2 x$$3 	anh^2 x + 20 	anh x = 39$

If $\frac{5 \sinh 2x}{7+6 \cosh 2x} = \frac{3}{2}$,then $3 \tanh^2 x + 20 \tanh x = $

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