If 5sinhx-coshx=5 find tanhx

Solution:

If $5 \sinh x-\cosh x=5$ so, find $\tanh x$

Given, $5 \sinh x-\cosh x=5$

Dividing by $cosh x$,

we get, $5 \tanh x-1=5 \operatorname{sech} x$

Squaring both sides,

we get $(5 \tanh x-1)^{2}=25 \operatorname{sech}^{2} x$

$= 25 \tanh ^{2} x+1-10 \tanh ^{2} x=25\left(1-\tanh ^{2} x\right)$

$= 50 \tanh ^{2} …