Question

Question #6d140

Answer 1

You're almost there. Just use the fact that `cos^{2}(x)=1-sin^{2}(x)` and `\cosh^{2}(y)=1+sinh^{2}(y)` to substitute and simplify.

`|\sin(z)|^{2}=\cos^{2}(x)\sinh^{2}(y)+\sin^{2}(x)\cosh^{2}(y)=(1-\sin^{2}(x))\sinh^{2}(y)+\sin^{2}(x)(1+\sinh^{2}(y))=\sinh^{2}(y)-\sin^{2}(x)\sinh^{2}(y)+\sin^{2}(x)+\sin^{2}(x)\sinh^{2}(y)=\sin^{2}(x)+\sinh^{2}(y)`