document.write( "Question 717569: how do you simplify 1+sinx(-sinx)-cosx(cosx)/(1+sinx)^2 \n" ); document.write( "

Algebra.Com's Answer #440444 by jsmallt9(3758) $\"\"$ $\"About$

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How much of \"1+sinx(-sinx)-cosx(cosx)\" is in the numerator of the fraction? Please put numerators and denominators in parentheses to make it clear. Clearly posted problems get quicker responses.

\n" ); document.write( "If by chance all of \"1+sinx(-sinx)-cosx(cosx)\" is in the numerator (IOW, the expression is just one big fraction) then the answer is 0. Here's how:
\n" ); document.write( " $\"%281%2Bsin%28x%29%28-sin%28x%29%29-cos%28x%29%28cos%28x%29%29%29%2F%281%2Bsin%28x%29%29%5E2\"$
\n" ); document.write( "Multiplying in the numerator:
\n" ); document.write( " $\"%281-sin%5E2%28x%29-cos%5E2%28x%29%29%2F%281%2Bsinx%29%5E2\"$
\n" ); document.write( "Since $\"1-sin%5E2%28x%29+=+cos%5E2%28x%29\"$ :
\n" ); document.write( " $\"%28cos%5E2%28x%29-cos%5E2%28x%29%29%2F%281%2Bsinx%29%5E2\"$
\n" ); document.write( "Subtracting:
\n" ); document.write( " $\"%280%29%2F%281%2Bsinx%29%5E2\"$
\n" ); document.write( "which equals 0.

\n" ); document.write( " \n" ); document.write( "

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