document.write( "Question 282124: show that 1+cos(x)/sin(x)=sin(x)/1-cos(x) \n" ); document.write( "
Algebra.Com's Answer #204954 by dabanfield(803)\"\" \"About 
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show that 1+cos(x)/sin(x)=sin(x)/1-cos(x)\r
\n" ); document.write( "\n" ); document.write( "Let's start with the rigth-hand side above:\r
\n" ); document.write( "\n" ); document.write( "sin(x)/(1-cos(x))\r
\n" ); document.write( "\n" ); document.write( "Multiply above numerator and denominator by 1+cos(x):\r
\n" ); document.write( "\n" ); document.write( "(sin(x)*(1+cos(x))/((1-cos(x))*(1+cos(x))\r
\n" ); document.write( "\n" ); document.write( "(sin(x)+sin(x)*cos(x))/(1^2 -cos(x)+cos(x)-cos(x)^2)\r
\n" ); document.write( "\n" ); document.write( "(sin(x)+sin(x)*cos(x))/(1-cos(x)^2)\r
\n" ); document.write( "\n" ); document.write( "Using the identity sin(x)^2 + cos(x)^2 = 1 we know sin(x)^2 = 1 - cos(x)^2. So the above becomes:\r
\n" ); document.write( "\n" ); document.write( "(sin(x)+sin(x)*cos(x))/(sin(x)^2 =\r
\n" ); document.write( "\n" ); document.write( "(sin(x)/sin(x)^2) + (sin(x)*cos(x)/sin(x)^2) =
\n" ); document.write( "1/sin(x) + cos(x)/sin(x) =\r
\n" ); document.write( "\n" ); document.write( "(1 + cos(x))/sin(x)
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