document.write( "Question 1071242: Given: \"sin%28theta%29-cos%28theta%29=1%2F2\"
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Algebra.Com's Answer #686342 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\"sin%28theta%29-cos%28theta%29=1%2F2\"\r\n" );
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document.write( "Square both sides\r\n" );
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document.write( "\"sin%28theta%29%5E2-2sin%28theta%29cos%28theta%29%2Bcos%5E2%28theta%29=1%2F4\"\r\n" );
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document.write( "\"sin%28theta%29%5E2%2Bcos%5E2%28theta%29-2sin%28theta%29cos%28theta%29=1%2F4\"\r\n" );
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document.write( "\"1-2sin%28theta%29cos%28theta%29=1%2F4\"\r\n" );
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document.write( "\"1-sin%282theta%29=1%2F4\"\r\n" );
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document.write( "\"-sin%282theta%29=-3%2F4\"\r\n" );
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document.write( "\"sin%282theta%29=3%2F4\"\r\n" );
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document.write( "\"cos%282theta%29=+%22%22+%2B-+sqrt%281-sin%5E2%282theta%29%29\"\r\n" );
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document.write( "\"cos%282theta%29=+%22%22+%2B-+sqrt%281-%283%2F4%29%5E2%29\"\r\n" );
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document.write( "\"cos%282theta%29=+%22%22+%2B-+sqrt%281-9%2F16%29\"\r\n" );
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document.write( "\"cos%282theta%29=+%22%22+%2B-+sqrt%2816%2F16-9%2F16%29\"\r\n" );
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document.write( "\"cos%282theta%29=+%22%22+%2B-+sqrt%287%2F16%29\"\r\n" );
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document.write( "\"cos%282theta%29=+%22%22+%2B-+sqrt%287%29%2F4\"\r\n" );
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document.write( "\"cos%282theta%29=cos%5E2%28theta%29-sin%5E2%28theta%29\"\r\n" );
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document.write( "\"sin%5E2%28theta%29-cos%5E2%28theta%29=-cos%282theta%29\"\r\n" );
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document.write( "\"%281%2F2%29%28sin%28theta%29%2Bcos%28theta%29%5E%22%22%29=%28%22%22+%2B-+sqrt%287%29%29%2F4\"\r\n" );
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document.write( "\"sin%28theta%29%2Bcos%28theta%29=%28%22%22+%2B-+sqrt%287%29%29%2F2\"\r\n" );
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document.write( "That's the proof.\r\n" );
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document.write( "----------------------------------------------------------------\r\n" );
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document.write( "Notice that the right side could be either positive or negative,\r\n" );
document.write( "although you did not have the ± originally.  I included it above).\r\n" );
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document.write( "To show that it can  be either positive or negative:\r\n" );
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document.write( "By calculator the solutions between 0° and 360° are approximately\r\n" );
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document.write( "\"theta=%2265.70481105%B0%22\" and \"theta=%22204.2951889%B0%22\"\r\n" );
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document.write( "and \"sqrt%287%29%2F2=1.322874656\"\r\n" );
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document.write( "For \"theta=%2265.70481105%B0%22\"\r\n" );
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document.write( "\"sin%2865.70481105%29%2Bcos%2865.70481105%29=+1.322875656\"\r\n" );
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document.write( "and for \"theta=%22204.2951889%B0%22\",\r\n" );
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document.write( "\"sin%28%22204.2951889%B0%22%29%2Bcos%28%22204.2951889%B0%22%29=+-1.322875656\"\r\n" );
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document.write( "So you see that it can be positive or negative.\r\n" );
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document.write( "Edwin
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