You can put this solution on YOUR website! simplify cos x/(csc x + 1)
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cos(x)/((1/sin(x))+1)
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cos(x)/(1+sin(x)/sin(x)
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= [cos(x)(sin(x))/(1+sin(x)
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= (1/2)sin(2x)/(1+sin(x)
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Can't say it look more simplified, but it has changed.
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Cheers,
Stan H.