document.write( "Question 1034445: Please help me to prove using de Moivre's Theorem that \"+4%2Asin%5E3+%28x%29+=3%2Asin%28x%29+-sin%283%2Ax%29\" \n" ); document.write( "
Algebra.Com's Answer #649133 by robertb(5830)\"\" \"About 
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,after applying de Moivre's and direct expansion.\r
\n" ); document.write( "\n" ); document.write( "= \"cos%5E3%28x%29%2B3icos%5E2%28x%29sinx+-+3cosx%2Asin%5E2%28x%29+-+isin%5E3%28x%29\".\r
\n" ); document.write( "\n" ); document.write( "Now equate the imaginary parts of the first complex quantity and the last complex quantity.\r
\n" ); document.write( "\n" ); document.write( "==> \r
\n" ); document.write( "\n" ); document.write( "==> \"sin%283x%29+=+3sinx+-+3sin%5E3%28x%29+-+sin%5E3%28x%29+=+3sinx+-+4sin%5E3%28x%29\"\r
\n" ); document.write( "\n" ); document.write( "==> \"sin%283x%29+=+3sinx+-+4sin%5E3%28x%29\", or \"highlight%284sin%5E3%28x%29+=+3sinx+-+sin%283x%29%29\".\r
\n" ); document.write( "\n" ); document.write( "As an added bonus, what would happen if you equated the real parts of the first complex quantity and the last complex quantity? Try it out yourself.
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