document.write( "Question 817280: Simplify csc(x)-cos^2(x)csc(x) \n" ); document.write( "

Algebra.Com's Answer #491971 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"csc%28x%29-cos%5E2%28x%29csc%28x%29\"$
\n" ); document.write( "Here's one way...
\n" ); document.write( "Factor out csc(x):
\n" ); document.write( " $\"csc%28x%29%281-cos%5E2%28x%29%29\"$
\n" ); document.write( "We should recognize that $\"1-cos%5E2%28x%29+=+sin%5E2%28x%29\"$ :
\n" ); document.write( " $\"csc%28x%29%28sin%5E2%28x%29%29\"$
\n" ); document.write( "Since csc and sin are reciprocals of each other we can replace csc with 1/sin:
\n" ); document.write( " $\"%281%2Fsin%28x%29%29%28sin%5E2%28x%29%29\"$
\n" ); document.write( "The sin in the denominator cancels out with one of the factors of sin in $\"sin%5E2%28x%29\"$ leaving:
\n" ); document.write( "sin(x)
\n" ); document.write( " \n" ); document.write( "

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