document.write( "Question 635009: sin(3x)/sin x= 2 cos(2x)+1\r
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Algebra.Com's Answer #400055 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"sin%283x%29%2Fsin%28x%29\" = \"2cos%282x%29+%2B+1\"\r\n" );
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document.write( "We work with the left side\r\n" );
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document.write( "We write 3x as 2x+x\r\n" );
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document.write( "\"sin%282x%2Bx%29%2Fsin%28x%29\" \r\n" );
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document.write( "Use the identity \"sin%28alpha%2Bbeta%29=sin%28alpha%29cos%28beta%29%2Bcos%28alpha%29sin%28beta%29\"\r\n" );
document.write( "with \"alpha=2x\" and \"beta=x\"\r\n" );
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document.write( "\"+%28sin%282x%29cos%28x%29%2Bcos%282x%29sin%28x%29%29%0D%0A%0D%0A%2Fsin%28x%29\"\r\n" );
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document.write( "Break into the sum of two fractions with the same denominator\r\n" );
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document.write( "\"sin%282x%29cos%28x%29%2Fsin%28x%29\" + \"cos%282x%29sin%28x%29%2Fsin%28x%29\"\r\n" );
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document.write( "Cancel the sin(x)'s in the second term\r\n" );
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document.write( "\"sin%282x%29cos%28x%29%2Fsin%28x%29\" + \"cos%282x%29cross%28sin%28x%29%29%2Fcross%28sin%28x%29%29\"\r\n" );
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document.write( "\"sin%282x%29cos%28x%29%2Fsin%28x%29\" + \"cos%282x%29\"\r\n" );
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document.write( "Use the identity \"sin%282theta%29=2sin%28theta%29cos%28theta%29\" for \"sin%282x%29\"\r\n" );
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document.write( "\"2sin%28x%29cos%28x%29cos%28x%29%2Fsin%28x%29\" + \"cos%282x%29\"\r\n" );
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document.write( "Cancel the sin(x)'s in the first term\r\n" );
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document.write( "\"2cross%28sin%28x%29%29cos%28x%29cos%28x%29%2Fcross%28sin%28x%29%29\" + \"cos%282x%29\"\r\n" );
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document.write( "\"2cos%28x%29cos%28x%29\" + \"cos%282x%29\"\r\n" );
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document.write( "\"2cos%5E2%28x%29\" + \"cos%282x%29\"\r\n" );
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document.write( "Use the identity \"cos%282theta%29=2cos%5E2%28theta%29-1\" solved for \"2cos%5E2%28theta%29\"\r\n" );
document.write( "or \"2cos%5E2%28theta%29=cos%282theta%29%2B1\"\r\n" );
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document.write( "\"cos%282x%29%2B1\" + \"cos%282x%29\"\r\n" );
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document.write( "Combine like terms:\r\n" );
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document.write( "\"2cos%282x%29+%2B+1\"\r\n" );
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document.write( "--------------------------\r\n" );
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document.write( "\"cot%28x%29%2F%28csc%28x%29%2B1%29\" = \"%28csc%28x%29-1%29%2F%28cot%28x%29%29\"\r\n" );
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document.write( "We work with the left side:\r\n" );
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document.write( "Multiply the left sides by the conjugate of the denominator\r\n" );
document.write( "over itself.  That is multiply by \"%28csc%28x%29-1%29%2F%28csc%28x%29-1%29\"\r\n" );
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document.write( "\"cot%28x%29%2F%28csc%28x%29%2B1%29\"·\"%28csc%28x%29-1%29%2F%28csc%28x%29-1%29\"\r\n" );
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document.write( "\"cot%28x%29%2F%28csc%28x%29%2B1%29%2A%28csc%28x%29-1%29%2F%28csc%28x%29-1%29\"\r\n" );
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document.write( "\"%28cot%28x%29%2A%28csc%28x%29-1%29%29%2F%28csc%5E2%28x%29-1%29\"\r\n" );
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document.write( "We use the identity \"1%2Bcot%5E2%28theta%29=csc%5E2%28theta%29\" to replace the\r\n" );
document.write( "\"csc%5E2%28x%29\" in the denominator.\r\n" );
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document.write( "\"%28cot%28x%29%2A%28csc%28x%29-1%29%29%2F%281%2Bcot%5E2%28x%29-1%29\"\r\n" );
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document.write( "\"%28cot%28x%29%2A%28csc%28x%29-1%29%29%2Fcot%5E2%28x%29\"\r\n" );
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document.write( "\"%28cross%28cot%28x%29%29%2A%28csc%28x%29-1%29%29%2Fcot%5Ecross%282%29%28x%29\"\r\n" );
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document.write( "\"%28csc%28x%29-1%29%2F%28cot%28x%29%29\"\r\n" );
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document.write( "Edwin
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