document.write( "Question 1207649: prove that (\sin (\theta )+\tan (\theta ))/(\csc (\theta )+\cot (\theta )) = sin(\theta ) tan (\theta ) \n" ); document.write( "
Algebra.Com's Answer #845631 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "By the way, that notation with backward slashes \"\\" is not compatible with \r\n" );
document.write( "this site, which is written with HTML, so there is no need using it here.\r\n" );
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document.write( "Here's an alternate proof, using the fact that any quantity multiplied by\r\n" );
document.write( "its reciprocal is always 1. \r\n" );
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document.write( "Start with the left side:\r\n" );
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document.write( "\"%28sin%28theta%29%2Btan%28theta%29%29%2F%28csc%28theta%29%2Bcot%28theta%29%29\"\r\n" );
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document.write( "Multiply top and bottom by the \"conjugate\" of the denominator:\r\n" );
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document.write( "\"expr%28%28sin%28theta%29%2Btan%28theta%29%29%2F%28csc%28theta%29%2Bcot%28theta%29%29%29\"\"%22%22%2A%22%22\"\"expr%28%28csc%28theta%29-cot%28theta%29%29%2F%28csc%28theta%29-cot%28theta%29%29%29\"\r\n" );
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document.write( "Use the fact that multiplying an expression by its reciprocal is always 1.\r\n" );
document.write( "Also the denominator is a well-known identity:\r\n" );
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document.write( "\"%28%0D%0A1-sin%28theta%29cot%28theta%29%2Btan%28theta%29csc%28theta%29-1%29%2F1\"\r\n" );
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document.write( "\"-sin%28theta%29cot%28theta%29%2Btan%28theta%29csc%28theta%29\"\r\n" );
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document.write( "\"-cos%28theta%29%2B1%2Fcos%28theta%29\"\r\n" );
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document.write( "\"%28-cos%5E2%28theta%29%2B1%29%2Fcos%28theta%29\"\r\n" );
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document.write( "\"sin%5E2%28theta%29%2Fcos%28theta%29\"\r\n" );
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document.write( "\"%28sin%28theta%29sin%28theta%29%29%2Fcos%28theta%29\"\r\n" );
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document.write( "\"sin%28theta%29%2Aexpr%28sin%28theta%29%2Fcos%28theta%29%29\"\r\n" );
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document.write( "\"sin%28theta%29%2Atan%28theta%29\"\r\n" );
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document.write( "Edwin
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