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henpen

  • 3 years ago

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

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  1. henpen
    • 3 years ago
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    How to get this to equal \[sin^2x+sinh^2y\]?

  2. henpen
    • 3 years ago
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    \[\sin^2x(1-\cosh^2y)=\sinh^2y(\cos^2x-1)\]

  3. henpen
    • 3 years ago
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    \[\cos^2x-1=-\sin^2x\] \[1-\cosh^2y=-\sinh^2y\] Yay!

  4. hartnn
    • 3 years ago
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    haha...u got it almost the same moment i got it..

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