Using the definitions of hyperbolic functions in terms of exponentials show that sech^2(x) = 1-tanh^2(x)

tanh(x) = ((ex-e-x)/2)/((ex+e-x)/2) 1 - tanh2(x) = 1-((ex-e-x)/(ex+e-x))2  = ((e2x+e-2x+2)-(e2x+e-2x-2))/(ex+e-x)2 = (2ex.2e-x)/(ex+e-x)2 = 4/(ex+e-x)2 = sech2x

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Answered by Chris B. Further Mathematics tutor

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