Question

If sechx=3/5 then tanh(2x)=?​

Answer 1

Answer:

answer is in this image

,

Answer 2

Answer:

$tanh(2x) = \frac{40}{41}$

Step-by-step explanation:

Given :

$sech(x) \: = \: \frac{3}{5}$

Therefore,

$cosh(x) \: = \frac{5}{3}$

$sinh(x) \: = \sqrt{ {cosh}^{2}(x) - 1}$

$sinh(x) \: = \sqrt{ \frac{25 - 9}{9} } = \frac{4}{3}$

$sinh(2x) \: = 2sinh(x)cosh(x) \: = 2 \times \frac{4}{3} \times \frac{5}{3} = \frac{40}{9}$

$cosh(2x) \: = \sqrt{1 + {sinh}^{2}(2x) } = \sqrt{1 + \frac{1600}{81} } = \frac{41}{9}$

$tanh(2x) = \frac{sinh(2x)}{cosh(2x)} = \frac{ \frac{40}{9} }{ \frac{41}{9} } = \frac{40}{41}$

I have considered only positive values. It is valid for negative values also.