cosh z = e z + e − z 2 {\displaystyle \cosh z={\frac {e^{z}+e^{-z}}{2}}}
sinh z = e z − e − z 2 {\displaystyle \sinh z={\frac {e^{z}-e^{-z}}{2}}}
cosh i z = cos z {\displaystyle \cosh iz=\cos z}
sinh i z = i sin z {\displaystyle \sinh iz=i\sin z}
tanh i z = i tan z {\displaystyle \tanh iz=i\tan z}
cosh ( x + y ) = cosh x cosh y + sinh x sinh y {\displaystyle \cosh(x+y)=\cosh x\cosh y+\sinh x\sinh y}
sinh ( x + y ) = sinh x cosh y + cosh x sinh y {\displaystyle \sinh(x+y)=\sinh x\cosh y+\cosh x\sinh y}
cosh ( x − y ) = cosh x cosh y − sinh x sinh y {\displaystyle \cosh(x-y)=\cosh x\cosh y-\sinh x\sinh y}
sinh ( x − y ) = sinh x cosh y − cosh x sinh y {\displaystyle \sinh(x-y)=\sinh x\cosh y-\cosh x\sinh y}
