Transcription of 3.6 The hyperbolic identities - mathcentre.ac.uk
1 hyperbolic identitiesIntroductionThe hyperbolic functions satisfy a number of identities . These allow expressions involving thehyperbolic functions to be written in different, yet equivalent forms. Several commonly usedidentities are given on this hyperbolic identitiescoshx=ex+ e x2,sinhx=ex e x2tanhx=sinhxcoshx=ex e xex+ e xsechx=1coshx=2ex+ e xcosechx=1sinhx=2ex e xcothx=coshxsinhx=1tanhx=ex+ e xex e xcosh2x sinh2x= 11 tanh2x= sech2xcoth2x 1 = cosech2xsinh(x y) = sinhxcoshy coshxsinhycosh(x y) = coshxcoshy sinhxsinhytanh(x y) =tanhx tanhy1 tanhxtanhysinh 2x= 2 sinhxcoshxcosh 2x= cosh2x+ sinh2xcosh2x=cosh 2x+ 12sinh2x=cosh 2x Pearson Education Ltd2000
