How do you verify $tanh x/(cosh x - sinh x tanh x) = sinh x$ ?

Question

1974 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-05T20:35:40

see below

Left Side: $=(sinhx/coshx)/(coshx-(sinhx*sinhx/coshx)$

$=(sinhx/coshx)/(coshx-sinh^2x/(coshx))$

$=(sinhx/coshx)/((cosh^2x-sinh^2x)/(coshx))$

$=sinhx/coshx * coshx/(cosh^2x-sinh^2x)$

$=sinhx/(cosh^2x-sinh^2x)$

$=sinhx/1$

$=sinhx$

$=$ Right Side

How do you verify tanh x/(cosh x - sinh x tanh x) = sinh xtanh x/(cosh x - sinh x tanh x) = sinh x?