document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=586529>Question 586529</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to prove that cos3x= 4cos^3x - 3cosx ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #373802 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=373802\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Use the Cosine of the Sum and the Cosine and Sine of Double Angles.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos\left(\phi\ +\ \varphi\right)\ =\ \cos\left(\phi\right)\cos\left(\varphi\right)\ -\ \sin\left(\phi\right)\sin\left(\varphi\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos\left(2\varphi\right)\ =\ \cos^2\left(\varphi\right)\ -\ \sin^2\left(\varphi\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin\left(2\varphi\right)\ =\ 2\sin\left(\varphi\right)\cos\left(\varphi\right)\"> \r<BR>\n" );
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document.write( "Then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos\left(3x\right)\ =\ \cos\left(2x\ +\ x\right)\">\r<BR>\n" );
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document.write( "So\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos\left(2x\ +\ x\right)\ =\ \cos\left(2x)\cos\left(x\right)\ -\ \sin\left(2x\right)\sin\left(x\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos\left(2x\right)\cos\left(x\right)\ -\ \sin\left(2x\right)\sin\left(x\right)\ =\ \left[\cos^2(x)\ -\ \sin^2{x}\right]\cos(x)\ -\ \left[2\sin(x)\cos{x}\right]\sin(x)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos^3(x)\ -\ \sin^2{x}\cos(x)\ -\ 2\sin^2(x)\cos{x}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos^3(x)\ -\ 3\sin^2{x}\cos(x)\">\r<BR>\n" );
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document.write( "Now use the Pythagorean Identity:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos^3(x)\ -\ 3\sin^2{x}\cos(x)\ =\ \cos^3(x)\ -\ 3\left(1\ -\ \cos^2{x}\right)\cos(x)\">\r<BR>\n" );
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document.write( "Distribute and collect terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \cos^3(x)\ -\ 3\left(1\ -\ \cos^2{x}\right)\cos(x)\ =\ \underline{4\cos^3(x)\ -\ 3\cos(x)}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ QED\">\r<BR>\n" );
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document.write( "John<BR>\n" );
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document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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