document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=443331>Question 443331</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that each is an identity\r<BR>\n" );
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document.write( "sin 3 x = 3 sin x - 4 sin^3 x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #305795 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=305795\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the sum formula for sine:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin{(3x)} = \sin(2x + x) = \sin(2x)\cos(x) + \sin(x)\cos(2x)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE = 2\sin(x)\cos(x)\cos(x) + \sin(x)(\cos^2(x) - \sin^2(x))\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE = 2\sin(x)\cos^2(x) + \sin(x)\cos^2(x) - \sin^3(x)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE = 3\sin(x)\cos^2(x) - \sin^3(x)\">\r<BR>\n" );
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document.write( "Replace cos^2(x) with 1 - sin^2(x):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE = 3\sin(x)(1 - \sin^2(x)) - \sin^3(x)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE = 3\sin(x) - 3\sin^3(x) - \sin^3(x)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE = 3\sin(x) - 4\sin^3(x)\">\r<BR>\n" );
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document.write( "Hence, the statement is an identity. </SPAN>\n" );
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