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Full Version: Trig vs hyperbolic handling differences in Prime CAS
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I posted this previously, but received no response so I'm trying again .

When I enter COS(x)^2+SIN(x)^2 in CAS I get the result 1, which is correct since this result is true regardless of the value of x. However, if I enter COSH(x)^2-SINH(x)^2 in CAS I should also get 1 as a result, however, I simply get COSH(x)^2-SINH(x)^2 as a result instead. If I replace x with a numerical value instead, then I get the proper result of 1. Why ? And yes I am in radians mode and have Exact unchecked when I do this.

Try using hyp2exp:

simplify(hyp2exp(cosh(x)^2-sinh(x)^2))

Gives you the answer you are looking for.

Thank you very much. Giving it some thought, this makes a lot of sense because while trig functions like cosine and sine are primary, hyperbolics like cosh and sinh are derived from the exponential function, which is primary.

Agreed. There is value in seeing the intermediate result of:

((exp(x)+1/exp(x))/2)^2-((exp(x)-1/exp(x))/2)^2