sin h2 =2sinh 2coshz

Question

solve this equation sin h2 = 2sinh 2coshz

Answer 1

I think this is supposed to be the identity:

sinh(2z)≡2sinh(z)cosh(z).

sinh(2z)=(e^2z-e^-2z)/2; sinh(z)=(e^z-e^-z)/2; cosh(z)=(e^z+e^-z)/2;

therefore, sinh(z)cosh(z)=(e^2z-e^-2z)/4=½sinh(2z), and sinh(2z)=2sinh(z)cosh(z) QED.