document.write( "Question 552128: Prove the following identity:\r
\n" ); document.write( "\n" ); document.write( "2sin(x+y)sin(x-y) = cos2y-cos2x \n" ); document.write( "
Algebra.Com's Answer #360139 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "This is one tough identity! It requires very unusual substitutions,\r\n" );
document.write( "additions and subtractions of the same quantities.\r\n" );
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document.write( "2sin(x+y)sin(x-y) = cos(2y)-cos(2x)\r\n" );
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document.write( "                  = cos(y+y) - cos(x+x)\r\n" );
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document.write( "                  = cos(y+y+x-x) - cos(x+x+y-y)\r\n" );
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document.write( "                  = cos[(x+y)-(x-y)] - cos[(x+y)+(x-y)]\r\n" );
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document.write( "     Use the identities cos(A∓B)=cos(A)cos(B)ąsin(A)sin(B)\r\n" );
document.write( "     with A=(x+y), B=(x-y)\r\n" );
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document.write( "= [cos(x+y)cos(x-y)+sin(x+y)sin(x-y)] - [cos(x+y)cos(x-y)-sin(x+y)sin(x-y)]    \r\n" );
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document.write( "= cos(x+y)cos(x-y) + sin(x+y)sin(x-y) - cos(x+y)cos(x-y) + sin(x+y)sin(x-y)\r\n" );
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document.write( "= cos(x+y)cos(x-y) + sin(x+y)sin(x-y) - cos(x+y)cos(x-y) + sin(x+y)sin(x-y)\r\n" );
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document.write( "                 = 2sin(x+y)(sin(x-y)\r\n" );
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document.write( "Edwin
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