document.write( "Question 695154: $\"sin%28x%29%2F%281%2Bcos%28x%29%29=%281-cos%28x%29%29%2Fsin%28x%29\"$ \n" ); document.write( "

Algebra.Com's Answer #428348 by pmatei(79) $\"\"$ $\"About$

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$\"sin%28x%29%2F%281%2Bcos%28x%29%29=%281-cos%28x%29%29%2Fsin%28x%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Because you deal with fractions you need to exclude from domain (possible answers) those values that will give you denominators equal to zero.\r
\n" ); document.write( "\n" ); document.write( " $\"1%2Bcos%28x%29+=0\"$
\n" ); document.write( " $\"cos%28x%29=-1\"$
\n" ); document.write( " $\"x=pi\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"sin%28x%29=0\"$
\n" ); document.write( " $\"x=0\"$ or $\"x=pi\"$ or $\"x=2%2Api\"$ \r
\n" ); document.write( "\n" ); document.write( "So for the interval [ $\"0\"$ , $\"2%2Api\"$ ] we cannot have as solutions 0, $\"pi\"$ , or $\"2%2Api\"$ .\r
\n" ); document.write( "\n" ); document.write( "Now as you do with any proportion, multiply on diagonal (butterfly method):\r
\n" ); document.write( "\n" ); document.write( " $\"%28sin%28x%29%29%5E2=%281-cos%28x%29%29%281%2Bcos%28x%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28sin%28x%29%29%5E2=1-%28cos%28x%29%29%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28sin%28x%29%29%5E2%2B%28cos%28x%29%29%5E2=1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"1=1\"$ \r
\n" ); document.write( "\n" ); document.write( "So this relation is true for every allowed value in the interval. \n" ); document.write( "

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