Friday, May 9, 2008

Whoops

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


-.-;