Answers>Further Mathematics>A Level>Article

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

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

Answered by Chris B. • Further Mathematics tutor

9246 Views

See similar Further Mathematics A Level tutors

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

Related Further Mathematics A Level answers

Find all square roots of the number 3 + 4i.

Differentiate artanh(x) with respect to x

How do I determine whether a system of 3 linear equations is consistent or not?

Unfortunately this box is to small to contain the question so please see the first paragraph of the answer box for the question.