document.write( "Question 1139613: Show that sin²x + sin²y + 2sinxsinycos(x+y) = sin²(x+y) \n" ); document.write( "
Algebra.Com's Answer #760301 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Let this be any triangle:\r\n" );
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document.write( "By the law of cosines:\r\n" );
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document.write( "(1)     \"c%5E2=a%5E2%2Bb%5E2-2%2Aa%2Ab%2Acos%28z%29\"\r\n" );
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document.write( "By the law of sines:\r\n" );
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document.write( "        \"a%2Fsin%28x%29=b%2Fsin%28y%29=c%2Fsin%28z%29\"\r\n" );
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document.write( "Let those equal to k\r\n" );
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document.write( "        \"a%2Fsin%28x%29=b%2Fsin%28y%29=c%2Fsin%28z%29=k\"\r\n" );
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document.write( "Then we have \r\n" );
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document.write( "Substitute in (1)\r\n" );
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document.write( "Divide through by k2:\r\n" );
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document.write( "        \"sin%5E2%28z%29=sin%5E2%28x%29%2Bsin%5E2%28y%29%29-2%2Asin%28x%29%2Asin%28y%29%2Acos%28z%29\"\r\n" );
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document.write( "Since x + y + z = 180°, z = 180°-x-y = 180°-(x+y)\r\n" );
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document.write( "Use the identities \"sin%28180%5E%22o%22-theta%29=sin%28theta%29\", and \"cos%28180%5E%22o%22-theta%29=-cos%28theta%29\":\r\n" );
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document.write( "          \r\n" );
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document.write( "Edwin
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