Question

\[sin(x+iy)=sin(x)cos(iy)+sin(iy)cos(x)=sin(x)cosh(y)+isinh(y)cos(x)\]

\[|sin(x+iy)|^2=?\]
\[|sin(x+iy)|=\sqrt{sin^2xcosh^2y+sinh^2ycos^2x}\]
\[|sin(x+iy)|^2=sin^2xcosh^2y+sinh^2ycos^2x\]

Answer 1

How to get this to equal \[sin^2x+sinh^2y\]?

Answer 2

\[\sin^2x(1-\cosh^2y)=\sinh^2y(\cos^2x-1)\]

Answer 3

\[\cos^2x-1=-\sin^2x\]
\[1-\cosh^2y=-\sinh^2y\]
Yay!

Answer 4

haha...u got it almost the same moment i got it..