document.write( "Question 1086313: If sin(x) + sin^2(x) = 1, then the value of cos^12(x) + 3cos^10(x) + 3cos^8(x) + cos^6(x) - 2 is ?
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Algebra.Com's Answer #700537 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"sin%28x%29+%2B+sin%5E2%28x%29+=+1\"\r\n" );
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document.write( "Subtracting sin2(x) from both sides,\r\n" );
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document.write( "\"sin%28x%29=1-sin%5E2%28x%29\"\r\n" );
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document.write( "Using a well-known Pythagorean identity,\r\n" );
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document.write( "\"sin%28x%29=cos%5E2%28x%29\"\r\n" );
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document.write( "Switching sides,\r\n" );
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document.write( "\"cos%5E2%28x%29=sin%28x%29\"\r\n" );
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document.write( "So, for that equation,\r\n" );
document.write( "raising both sides to the 6th power gives \"cos%5E12%28x%29=sin%5E6%28x%29\"\r\n" );
document.write( "raising both sides to the 5th power gives \"cos%5E10%28x%29=sin%5E5%28x%29\"\r\n" );
document.write( "raising both sides to the 4th power gives \"cos%5E8%28x%29=sin%5E4%28x%29\"\r\n" );
document.write( "raising both sides to the 3rd power gives \"cos%5E6%28x%29=sin%5E3%28x%29\"\r\n" );
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document.write( "So this\r\n" );
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document.write( "\"cos%5E12%28x%29+%2B+3cos%5E10%28x%29+%2B+3cos%5E8%28x%29+%2B+cos%5E6%28x%29+-+2\"\"%22%22=%22%22\"\r\n" );
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document.write( "upon substituting those, becomes\r\n" );
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document.write( "\"sin%5E6%28x%29+%2B+3sin%5E5%28x%29+%2B+3sin%5E4%28x%29+%2B+sin%5E3%28x%29+-+2\"\"%22%22=%22%22\"\r\n" );
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document.write( "Factoring out sin3(x) out of the first 4 terms,\r\n" );
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document.write( "\"%22%22=%22%22\"\r\n" );
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document.write( "Using the fact that (A+B)3 = A3+3A2B+3AB2+B3,\r\n" );
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document.write( "\"sin%5E3%28x%29%28sin%5E%22%22%28x%29+%2B+1%5E%22%22%5E%22%22%29%5E3+-+2\"\"%22%22=%22%22\"\r\n" );
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document.write( "Writing the product of cubes as the cube of the product,\r\n" );
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document.write( "\"%28sin%28x%29%28sin%28x%29+%2B+1%5E%22%22%29%5E%22%22%29%5E3+-+2\"\"%22%22=%22%22\"\r\n" );
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document.write( "Distributing,\r\n" );
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document.write( "\"%28sin%5E2%28x%29+%2B+sin%28x%29%5E%22%22%5E%22%22%29%5E3+-+2\"\"%22%22=%22%22\"\r\n" );
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document.write( "Reversing the terms,\r\n" );
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document.write( "\"%28sin%28x%29%5E%22%22%5E%22%22+%2B+sin%5E2%28x%29%29%5E3+-+2\"\"%22%22=%22%22\"\r\n" );
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document.write( "Notice that what's in the parentheses is exactly what is \r\n" );
document.write( "given as equal to 1 in the beginning, so\r\n" );
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document.write( "\"%281%29%5E3+-+2\"\"%22%22=%22%22\"\r\n" );
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document.write( "\"1-2\"\"%22%22=%22%22\"\r\n" );
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document.write( "\"-1\"\r\n" );
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document.write( "Edwin
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