theorem Th21: :: SIN_COS8:21

for y, z, w being Real holds
( sinh ((y + z) + w) = ((((((tanh y) + (tanh z)) + (tanh w)) + (((tanh y) * (tanh z)) * (tanh w))) * (cosh y)) * (cosh z)) * (cosh w) & cosh ((y + z) + w) = (((((1 + ((tanh y) * (tanh z))) + ((tanh z) * (tanh w))) + ((tanh w) * (tanh y))) * (cosh y)) * (cosh z)) * (cosh w) & tanh ((y + z) + w) = ((((tanh y) + (tanh z)) + (tanh w)) + (((tanh y) * (tanh z)) * (tanh w))) / (((1 + ((tanh z) * (tanh w))) + ((tanh w) * (tanh y))) + ((tanh y) * (tanh z))) )