document.write( "Question 1045772: Please help me solve these questions pls:
\n" ); document.write( "1. cos6x = 32cos^6 (x) -48cos^4 (x) +18cos^2 (x) -1
\n" ); document.write( "2. (sin(x+y)/cos(x-y)) +1 = ((1+tany)(1+cotx))/(cotx+tany)
\n" ); document.write( "3. 2cos^2 (3x) -sin7xsinx = 1+cos7xcosx\r
\n" ); document.write( "\n" ); document.write( "Thanks for your help :) \n" ); document.write( "
Algebra.Com's Answer #661289 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "1.   cos(3x) = cos(2x+x) = cos(2x)cos(x)-sin(2x)sin(x) =\r\n" );
document.write( "(2cos˛(x)-1)cos(x)-2sin(x)cos(x)sin(x) =\r\n" );
document.write( "2cosł(x)-cos(x)-2sin˛(x)cos(x) =\r\n" );
document.write( "2cosł(x)-cos(x)-2[1-cos˛(x)]cos(x) =\r\n" );
document.write( "2cosł(x)-cos(x)-2cos(x)+2cosł(x)\r\n" );
document.write( "4cosł(x)-3cos(x)\r\n" );
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document.write( "So cos(3x)=4cosł(x)-3cos(x) and cos(2x)=2cos˛(x)-1. \r\n" );
document.write( "So cos(6x)=2[cos(3x)]˛-1 or 2[4cosł(x)-3cos(x)]˛-1.\r\n" );
document.write( "We can expand it to become \r\n" );
document.write( "2[16cos6(x)-24cos4(x)+9cos˛(x)]-1 \r\n" );
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document.write( "Final result: cos(6x) = \r\n" );
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document.write( "32cos6(x) - 48cos4(x) + 18cos2(x) - 1\r\n" );
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document.write( "2.   \r\n" );
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document.write( "\"%281%5E%22%22%2Btan%28y%29%29%281%5E%22%22%2Bcot%28x%29%29\"\"%22%F7%22\"\"%28cot%28x%29%5E%22%22%2Btan%28y%29%29\"\r\n" );
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document.write( "\"%22%F7%22\"\"%28cos%28x%29%2Fsin%28x%29%2Bsin%28y%29%2Fcos%28y%29%29\"\r\n" );
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document.write( "\"%22%F7%22\"\"%28cos%28x%29cos%28y%29%2Bsin%28y%29sin%28x%29%29%2F%28sin%28x%29cos%28y%29%29\"\r\n" );
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document.write( "\"%22%F7%22\"\"%28cos%28x%29cos%28y%29%2Bsin%28x%29sin%28y%29%29%2F%28sin%28x%29cos%28y%29%29\"\r\n" );
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document.write( "\"%22%F7%22\"\"cos%28x-y%29%2F%28sin%28x%29cos%28y%29%29\"\r\n" );
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document.write( "\"%22%22%2A%22%22\"\"%28sin%28x%29cos%28y%29%29%2Fcos%28x-y%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28sin%28x%2By%29%2Bcos%28x-y%29%29%2F%28cos%28y%29sin%28x%29%29%29\"\"%22%22%2A%22%22\"\"%28sin%28x%29cos%28y%29%29%2Fcos%28x-y%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28sin%28x%2By%29%2Bcos%28x-y%29%29%2F%28cross%28cos%28y%29%29cross%28sin%28x%29%29%29%29\"\"%22%22%2A%22%22\"\"%28cross%28sin%28x%29%29cross%28cos%28y%29%29%29%2Fcos%28x-y%29\"\r\n" );
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document.write( "\"%28sin%28x%2By%29%2Bcos%28x-y%29%29%2F1\"\"%22%22%2A%22%22\"\"1%2Fcos%28x-y%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"sin%28x%2By%29%2Fcos%28x-y%29%2B%22%22%5E1cross%28cos%28x-y%29%29%2Fcross%28cos%28x-y%29%29\"\r\n" );
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document.write( "\"sin%28x%2By%29%2Fcos%28x-y%29%2B1\"\r\n" );
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document.write( "\"1%2Bsin%28x%2By%29%2Fcos%28x-y%29\"\r\n" );
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document.write( "----------------------\r\n" );
document.write( "\"2cos%5E2%283x%29+-sin%287x%29sin%28x%29+=+1%2Bcos%287x%29cos%28x%29\"\r\n" );
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document.write( "This one requires some tricks of subtracting and adding the\r\n" );
document.write( "same quantity to create a use for some double-angle identities. \r\n" );
document.write( "We work with the left side:\r\n" );
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document.write( "Subtract 1 and add 1 to create a use for the identity\r\n" );
document.write( "                \"cos%282theta%29=2cos%5E2%28theta%29-1\"\r\n" );
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document.write( "\"2cos%5E2%283x%29-1%2B1-sin%287x%29sin%28x%29\"\r\n" );
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document.write( "Using that identity, the first two terms become cos(6x) \r\n" );
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document.write( "\"cos%286x%29%2B1-sin%287x%29sin%28x%29\"\r\n" );
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document.write( "Subtract and add cos(7x)cos(x) to create a\r\n" );
document.write( "use for the identity \"cos%28alpha-beta%29=cos%28alpha%29cos%28beta%29%2Bsin%28alpha%29sin%28beta%29\"\r\n" );
document.write( " \r\n" );
document.write( "\"cos%286x%29%2B1-sin%287x%29sin%28x%29-cos%287x%29cos%28x%29%2Bcos%287x%29cos%28x%29\"\r\n" );
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document.write( "Factor a \"-\" out of 3rd and 4th terms:\r\n" );
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document.write( "Swap the terms in the parentheses to recognize the identity:\r\n" );
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document.write( "Use the identity\r\n" );
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document.write( "\"cos%286x%29%2B1-cos%287x-x%29%2Bcos%287x%29cos%28x%29\"\r\n" );
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document.write( "7x-x = 6x\r\n" );
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document.write( "\"cos%286x%29%2B1-cos%286x%29%2Bcos%287x%29cos%28x%29\"\r\n" );
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document.write( "Cancel the two opposite terms\r\n" );
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document.write( "\"cross%28cos%286x%29%29%2B1-cross%28cos%286x%29%29%2Bcos%287x%29cos%28x%29\"\r\n" );
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document.write( "\"1%2Bcos%287x%29cos%28x%29\"\r\n" );
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document.write( "Tricky, huh?\r\n" );
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document.write( "Edwin
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