Prove that sin(j*x) = j*(sinh(x)):
This is what I did:
sin(j*x) = (e^j*x - e^-j*x) / 2*j
j*(sinh(x)) = (e^x - e^-x) / 2
Therefore:
(e^j*x - e^-j*x) / 2*j = j*(e^x - e^-x) / 2
Whoops... If your not shaking your head already:
sin(j*x) = (e^jb - e^-jb) / 2j , where b = jx
sin(j*x) = (e^j*(j*x) - e^-j*(j*x)) / 2*j
sin(j*x) = (e^-x) - e^x)) / 2*j
sin(j*x) = ((e^-x) - e^x)) / 2*j ) * (j/j)
sin(j*x) = j*((e^-x - e^x)) / -2
sin(j*x) = j*(e^x) - e^-x)) / 2*j
-.-;