document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=592883>Question 592883</A>: <I><SPAN STYLE=\"word-break: break-all;\"> verifyin trigonometric identities.<BR>\n" );
document.write( "(1/1-sinx)+(1/1+sinx)=2sec^2x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #376123 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=376123\">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 \ \ \ \ \ \ \ \ \ \ \frac{1}{1\ -\ \sin x}\ +\ \frac{1}{1\ +\ \sin x}\ \equiv^?\ 2\sec^2x\">\r<BR>\n" );
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document.write( "The LCD in the LHS is the product of the two denominators.  Since they are binomial conjugates, the product is the difference of two squares.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{1\ +\ \sin x\ +\ 1\ -\ \sin x}{1\ -\ \sin^2x}\ \equiv^?\ 2\sec^2x\">\r<BR>\n" );
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document.write( "Apply the Pythagorean Identity to the LHS denominator and simplify the LHS numerator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{2}{\cos^2x}\ \equiv^?\ 2\sec^2x\">\r<BR>\n" );
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document.write( "Recall that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{\cos\varphi}\ \equiv\ \sec\varphi\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2\sec^2x\ \equiv\ 2\sec^2x\">\r<BR>\n" );
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document.write( "Q.E.D.\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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