document.write( "Question 1011603: prove that sin^6 theta = -1/32 (cos 6 theta - 6 cos 4 theta + 16 cos 2 theta - 10). \n" ); document.write( "
Algebra.Com's Answer #627347 by Edwin McCravy(20064)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "It isn't true!  So instead of proving it, let's disprove it:\r\n" );
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document.write( "\"sin%5E6%28theta%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "We'll just prove that it isn't true by substituting \"theta=0\"\r\n" );
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document.write( "\"sin%5E6%280%29\"\"%22%22=%22%22\"\"expr%28-1%2F32%29%28cos%286%2A0%29%5E%22%22+-+6cos%284%2A0%29+%2B+16cos%282%2A0%29+-+10%29\"\r\n" );
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document.write( "\"sin%5E6%280%29\"\"%22%22=%22%22\"\"expr%28-1%2F32%29%28cos%280%29%5E%22%22+-+6cos%280%29+%2B+16cos%280%29+-+10%29\"\r\n" );
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document.write( "sin(0) = 0 and cos(0) = 1, so\r\n" );
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document.write( "\"0%5E6\"\"%22%22=%22%22\"\"expr%28-1%2F32%29%281+-+6%281%29+%2B+16%281%29+-+10%29\"\r\n" );
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document.write( "\"0\"\"%22%22=%22%22\"\"expr%28-1%2F32%29%281+-+6+%2B+16+-+10%29\"\r\n" );
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document.write( "\"0\"\"%22%22=%22%22\"\"expr%28-1%2F32%29%281%29\"\r\n" );
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document.write( "\"0\"\"%22%22=%22%22\"\"-1%2F32\"\r\n" );
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document.write( "So that is false.  Did you perhaps copy it wrong?\r\n" );
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document.write( "Edwin
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