document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=27039>Question 27039</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "Please can you help me find the general solution in radians of the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin2x+-+1+=+cos2x ALIGN=MIDDLE  ALT=\"sin2x+-+1+=+cos2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you very much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #14702 by </B><A HREF=/tutors/aboutme.mpl?userid=kev82><B>kev82(151)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kev82><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=14702\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi,\r<BR>\n" );
document.write( "\n" );
document.write( "There is probably a trig identity that solves this immediatly, but I'm useless at remembering them, I only know 3 or 4 myself. So I looked for a cleverer solution. And after staring for a few minutes, I found it.\r<BR>\n" );
document.write( "\n" );
document.write( "Square your equation, and see what you get.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?(\sin 2x - \cos 2x)^2 = 1^2\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\sin^2 2x + \cos^2 2x -2\sin 2x\cos 2x = 1\">\r<BR>\n" );
document.write( "\n" );
document.write( "Now using, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\cos^2 + \sin^2 = 1\">, and subtracting one from both sides, we get the much nicer\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?-2\sin 2x\cos 2x=0\">\r<BR>\n" );
document.write( "\n" );
document.write( "This can be solved either by using the sine addition formula and saying that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\sin 4x=0\"> or by saying that either <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\sin 2x=0\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\cos 2x=0\">. Either way you should get the solutions as\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?x=\frac{\pi}{2}n,\frac{\pi}{4}(1+2n),n\in\{0,1,2,3}\">\r<BR>\n" );
document.write( "\n" );
document.write( "'Wait! Zero isn't a solution' I hear you shout. This is true, but think back to when we squared the equation. We have also solved <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\sin 2x - \cos 2x = -1\"> because it squares to the same thing. So you have to check which solutions satisfy your original equation and then you're done.\r<BR>\n" );
document.write( "\n" );
document.write( "Hope that helps. (If you do find an easier way to solve it I would be interested to know)\r<BR>\n" );
document.write( "\n" );
document.write( "Kev </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );