Certain trig and hyperbolic functions will not cancel to 1 with their inverses.
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Enter sin(x)*1/sin(x) and it will yield 1. Likewise tan(x)*1/tan(x) yields 1.
But enter cos(x)*1/cos(x) and it will yield cos(x)*sec(x).
Likewise sinh(x)*1/sinh(x) yields sinh(x)*csch(x), cosh(x)*1/cosh(x) yields cosh(x)*sech(x), and tanh(x)*1/tanh(x) tanh(x)*coth(x).
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