This page introduces the hyperbolic functions and their inverses in each CAS.
>> syms x >> simplify( cosh(x)^2 - sinh(x)^2 ) ans = 1 >> simplify( sinh(2*x) - 2*sinh(x)*cosh(x) ) ans = 0 >> simplify( cosh(x)^2 + sinh(x)^2 - cosh(2*x) ) ans = 0 >> simplify( cosh(x)^2 - 1/2*(cosh(2*x)+1) ) ans = 0 >> simplify( sinh(x)^2 - 1/2*(cosh(2*x)-1) ) ans = 0 >> simplify( tanh(x)^2 + sech(x)^2 ) ans = 1 >> simplify( coth(x)^2 - csch(x)^2 ) ans = 1
>> syms x >> diff([sinh(x) cosh(x) tanh(x) coth(x) sech(x) csch(x)]) ans = [ cosh(x), sinh(x), 1 - tanh(x)^2, 1 - coth(x)^2, -sinh(x)/cosh(x)^2, -cosh(x)/sinh(x)^2] >> int([sinh(x) cosh(x) tanh(x) coth(x) sech(x) csch(x)]) ans = [ cosh(x), sinh(x), log(cosh(x)), log(sinh(x)), 2*atan(exp(x)), log(tanh(x/2))]
>> syms x >> diff([asinh(x) acosh(x) atanh(x) acoth(x) asech(x) acsch(x)]) ans = [ 1/(x^2 + 1)^(1/2), 1/(x^2 - 1)^(1/2), -1/(x^2 - 1), -1/(x^2 - 1), -1/(x^2*(1/x^2 - 1)^(1/2)), -1/(x^2*(1/x^2 + 1)^(1/2))] >> pretty( ans ) +- -+ | 1 1 1 1 1 1 | | -----------, -----------, - ------, - ------, - ----------------, - ---------------- | | 2 1/2 2 1/2 2 2 2 / 1 \1/2 2 / 1 \1/2 | | (x + 1) (x - 1) x - 1 x - 1 x | -- - 1 | x | -- + 1 | | | | 2 | | 2 | | | \ x / \ x / | +- -+
