(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show [tex]|sin z|^2 = \frac{1}{2}[cosh(2y)-cos(2x)][/tex]

2. Relevant equations

[tex]cosh2y = cosh^2y+sinh^2y[/tex]

[tex]cos2x = cos^2x-sin^2x[/tex]

3. The attempt at a solution

Here is what I have so far

[tex]|sinz|^2=|sin(x+iy)|^2=|sin(x)cosh(y)+icos(x)sinh(y)|^2[/tex]

[tex]=sin^2(x)cosh^2(y)+cos^2(x)sinh^2(y)[/tex]

[tex]=sin^2(x)cosh^2(y)+cos^2(x)sinh^2(y)-sin^2(x)sinh^2(y)+sin^2(x)sinh^2(y)[/tex]

[tex]=sin^2(x)[cosh^2(y)+sinh^2(y)]+sinh^2(y)[cos^2(x)-sin^2(x)][/tex]

[tex]=sin^2(x)cosh(2y)+sinh^2(y)cos(2x)[/tex]

how should i proceed?

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# Homework Help: Complex Trig Identity

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