You can put this solution on YOUR website! (csc + sin)*(csc - sin) = cot^2 + cos^2
csc^2 - sin^2 = cos^2*(csc^2 + 1)
1 - sin^4 = cos^2*(1 + sin^2)
1 - sin^2 = cos^2
QED
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I'm still waiting for an example of working one side only affects the result.