document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=906155>Question 906155</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please show me how to prove the following identities...<BR>\n" );
document.write( "A) cos2x=2cos^2x-1<BR>\n" );
document.write( "B) cos2x=1-2sin^2x<BR>\n" );
document.write( "C) (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 #549652 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=549652\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> prove the following identities...<BR>\n" );
document.write( "A) cos2x=2cos^2x-1<BR>\n" );
document.write( "start with left side:<BR>\n" );
document.write( "cos2x=cos(x+x)<BR>\n" );
document.write( "=coscosx-sinxsinx<BR>\n" );
document.write( "=cos^2x-(1-cos^2x)=2cos^x-1<BR>\n" );
document.write( "verified: left side=right side<BR>\n" );
document.write( "..<BR>\n" );
document.write( "B) cos2x=1-2sin^2x<BR>\n" );
document.write( "start with left side:<BR>\n" );
document.write( "cos2x=cos(x+x)<BR>\n" );
document.write( "=coscosx-sinxsinx<BR>\n" );
document.write( "=cos^2x-sin^2x=1-sin^2x-sin^2x<BR>\n" );
document.write( "=1-2sin^2x<BR>\n" );
document.write( "verified: left side=right side<BR>\n" );
document.write( "..<BR>\n" );
document.write( "C) (1/1+sinx)+(1/1-sinx)=2sec^2x<BR>\n" );
document.write( "start with left side:<BR>\n" );
document.write( "(1/1+sinx)+(1/1-sinx)<BR>\n" );
document.write( "=(1-sinx+1+sinx)/(1+sinx)(1-sinx)<BR>\n" );
document.write( "=2/1-sin^2x<BR>\n" );
document.write( "=2/cos^2x<BR>\n" );
document.write( "=2sec^2x<BR>\n" );
document.write( "verified: left side=right side </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );