document.write( "Question 887566: Cos(n+1)x sin(n+2)x+cos(n+1)x cos(n+2)x=cosx \n" ); document.write( "
Algebra.Com's Answer #536775 by Edwin McCravy(20064)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "cos[(n+1)x]sin[(n+2)x]+cos[(n+1)x]cos[(n+2)x] = cos(x)\r\n" );
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document.write( "Let A = (n+1)x = nx+x\r\n" );
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document.write( "let B = (n+2)x = nx+2x\r\n" );
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document.write( "Then B-A = (nx+2x)-(nx+x) = nx+2x-nx-x = x\r\n" );
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document.write( "cos(A)sin(B)+cos(A)cos(B)=cos(B-A)\r\n" );
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document.write( "cos(A)sin(B)+cos(A)cos(B)=cos(B)cos(A)+sin(B)sin(A)\r\n" );
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document.write( "cos(A)sin(B) = sin(B)sin(A)\r\n" );
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document.write( "cos(A)sin(B) - sin(B)sin(A) = 0\r\n" );
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document.write( "sin(B)[cos(A)-sin(A)} = 0\r\n" );
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document.write( "sin(B) = 0;             cos(A)-sin(A) = 0\r\n" );
document.write( "                        -sin(A) = -cos(A)\r\n" );
document.write( "B = \"P%2Api\";               sin(A) = cos(A)\r\n" );
document.write( "where P is any integer  \"sin%28A%29%2Fcos%28A%29\"\"%22%22=%22%22\"\"cos%28A%29%2Fcos%28A%29\"\r\n" );
document.write( "(n+2)x = \"P%2Api\";          tan(A) = 1 \r\n" );
document.write( "x = \"P%2Api%2F%28n%2B2%29\"               A = \"pi%2F4%2BQ%2Api\" \r\n" );
document.write( "                        A = \"expr%28%281%2B4Q%29%2F4%29pi\"\r\n" );
document.write( "                        where Q is any integer\r\n" );
document.write( "                        n(x+1) = \"expr%28%281%2B4Q%29%2F4%29pi\"\r\n" );
document.write( "                        x+1 = \"expr%28%281%2B4Q%29%2F%284n%29%29pi\"\r\n" );
document.write( "                        x = \"expr%28%281%2B4Q%29%2F%284n%29%29pi-1\"    \r\n" );
document.write( "Edwin
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