quality:correction, stylistic:tone, linguistic:translation
Subtraction formulas

sinh (x − y) = sinh x cosh y − cosh x sinh y cosh (x − y) = cosh x cosh y − sinh x sinh y tanh (x − y) = tanh x − tanh y 1 − tanh x tanh y {\displaystyle {\begin{aligned}\sinh(x-y)&=\sinh x\cosh y-\cosh x\sinh y\\\cosh(x-y)&=\cosh x\cosh y-\sinh x\sinh y\\\tanh(x-y)&={\frac {\tanh x-\tanh y}{1-\tanh x\tanh y}}\\\end{aligned}}}

Also: sinh x − sinh y = 2 cosh (x + y 2) sinh (x − y 2) cosh x − cosh y = 2 sinh (x + y 2) sinh (x − y 2) {\displaystyle {\begin{aligned}\sinh x-\sinh y&=2\cosh \left({\frac {x+y}{2}}\right)\sinh \left({\frac {x-y}{2}}\right)\\\cosh x-\cosh y&=2\sinh \left({\frac {x+y}{2}}\right)\sinh \left({\frac {x-y}{2}}\right)\\\end{aligned}}}