document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=703822>Question 703822</A>: <I><SPAN STYLE=\"word-break: break-all;\"> establish each identity\r<BR>\n" );
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document.write( "sec(2 theta)= sec^2 theta over 2- sec^2 theta </SPAN>\n" );
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document.write( "sec(2 theta)= sec^2 theta over 2- sec^2 theta<BR>\n" );
document.write( "use x for theta<BR>\n" );
document.write( "sec2x=sec^2x/(2-sec^2x)<BR>\n" );
document.write( "start with right side<BR>\n" );
document.write( "sec^2x/(2-sec^2x)<BR>\n" );
document.write( "=1/cos^2x/(2-(1/cos^2x))<BR>\n" );
document.write( "=1/cos^2x/[(2cos^2x-1)/cos^2x]<BR>\n" );
document.write( "cancel out cos^2x<BR>\n" );
document.write( "=1/(2cos^2x-1)<BR>\n" );
document.write( "=1/(2(1-sin^2x)-1)<BR>\n" );
document.write( "=1/(2-2sin^2x-1)<BR>\n" );
document.write( "=1/1-2sin^2x<BR>\n" );
document.write( "=1/cos2x<BR>\n" );
document.write( "=sec2x<BR>\n" );
document.write( "verified: right side=left side </SPAN>\n" );
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