document.write( "Question 188283: Verify that this equation is an identity...
\n" ); document.write( "sin(4y) = 4sin(y)cos(y) - 8sin³(y)
\n" ); document.write( "I tried working on the right side and this is as far as I got.
\n" ); document.write( "First I factored...
\n" ); document.write( "4sinycosy(1 - 2sin^2y)
\n" ); document.write( "then I substituted 1-cos^2y for sin^y
\n" ); document.write( "4sinycosy(1-2(1-cos^2y)
\n" ); document.write( "4sinycisy(1-2+2cos^2y)
\n" ); document.write( "4sinycosy(2cos^2y-1)
\n" ); document.write( "and I don't know what to do next to get 4siny
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #141158 by Edwin McCravy(20062) $\"\"$ $\"About$

You can put this solution on YOUR website!
Verify that this equation is an identity...
\n" ); document.write( "sin(4y) = 4sin(y)cos(y) - 8sin³(y)
\n" ); document.write( "I tried working on the right side and this is as far as I got.\r
\n" ); document.write( "\n" ); document.write( "

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document.write( "Although the right side looks more complicated than\r\n" );
document.write( "the left side, it isn't, because 4y is much more \r\n" );
document.write( "complicated than just y. \r\n" );
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document.write( "So you'd do better to start with the left side and \r\n" );
document.write( "use these two double-angle formulas:\r\n" );
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document.write( "sin(2@) = 2sin(@)cos(@)  and   cos(2@) = 1 - 2sin²(@)\r\n" );
document.write( "\r\n" );
document.write( "----------------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "sin(4y)\r\n" );
document.write( "\r\n" );
document.write( "sin[2(2y)]\r\n" );
document.write( "\r\n" );
document.write( "2sin(2y)cos(2y)\r\n" );
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document.write( "2[2sin(y)cos(y)][1 - 2sin²(y)]\r\n" );
document.write( "\r\n" );
document.write( "4sin(y)cos(y)[1 - 2sin²(y)]\r\n" );
document.write( "\r\n" );
document.write( "4sin(y)cos(y) - 8sin³(y)\r\n" );
document.write( "\r\n" );
document.write( "Edwin

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