document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=602425>Question 602425</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Verify that the equation is an identity:\r<BR>\n" );
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document.write( "sin^4 - cos^4 = 2sin^2 - 1\r<BR>\n" );
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document.write( "Also please show the steps if you can. It will be a lot of help since I'm not at all good with Math. Thank you! :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #380225 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=380225\">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( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin^4(\varphi)\ -\ \cos^4(\varphi)\ \equiv^?\ 2\sin^2(\varphi)\ -\ 1\">\r<BR>\n" );
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document.write( "Factor the difference of two squares in the LHS:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(\sin^2(\varphi)\ -\ \cos^2(\varphi)\right)\left(\sin^2(\varphi)\ +\ \cos^2(\varphi)\right)\ \equiv^?\ 2\sin^2(\varphi)\ -\ 1\">\r<BR>\n" );
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document.write( "Note that the right-hand factor in the LHS is just the Pythagorean Identity:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(\sin^2(\varphi)\ -\ \cos^2(\varphi)\right)\left(1\right)\ \equiv^?\ 2\sin^2(\varphi)\ -\ 1\">\r<BR>\n" );
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document.write( "Then, using the Pythagorean identity again in the form <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \cos^2(\phi)\ =\ 1\ -\ \sin^2(\phi)\">, substitute:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sin^2(\varphi)\ -\ \left(1\ -\ \sin^2(\varphi)\right)\ \equiv^?\ 2\sin^2(\varphi)\ -\ 1\"> \r<BR>\n" );
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document.write( "Combine terms in the LHS:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2\sin^2(\varphi)\ -\ 1\ \equiv\ 2\sin^2(\varphi)\ -\ 1\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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