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

9138 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

Express cos(4x) in terms of powers of cos(x)

Differentiate: y=x^x

How to approximate the Binomial distribution to the Normal Distribution

f(x)=ln(x). Find the area underneath the curve f(x) between 1 and 2.