document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=836065>Question 836065</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I simply dont understand how to switch from the identites and solve these sort of questions... <BR>\n" );
document.write( "Prove the following identities:<BR>\n" );
document.write( "Cos^4 A + sin^4 A + 2sin^2 Ax cos^2 A =1<BR>\n" );
document.write( "CosA -sinA/ cos A+sinA = 1-2sinAcosA/1-2sin^2A<BR>\n" );
document.write( "CosA/sqroot(1+tanA) + sinA/ sqroot (1+cot^2 A) =1\r<BR>\n" );
document.write( "\n" );
document.write( "Please help, 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 #503940 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=503940\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Prove the following identities:<BR>\n" );
document.write( "Cos^4 A + sin^4 A + 2sin^2 Ax cos^2 A =1<BR>\n" );
document.write( "Factor:<BR>\n" );
document.write( "(cos^2+sin^2)(cos^2+sin^2) = 1<BR>\n" );
document.write( "1*1 = 1<BR>\n" );
document.write( "1 = 1<BR>\n" );
document.write( "--------------------------------------------------<BR>\n" );
document.write( "CosA -sinA/ cos A+sinA = 1-2sinAcosA/1-2sin^2A<BR>\n" );
document.write( "Left side: Multiply numerator and denominator by cos-sin<BR>\n" );
document.write( "Right side: In place of \"1\" put sin^2+cos^2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "(cos-sin)^2/(cos^2-sin^2) = [sin^2 -2sin*cos +cos^2]/(1-2sin^2)<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "Notice that the numerators are the same<BR>\n" );
document.write( "Notice that the denominators are the same<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "(cos^2-2cos*sin+sin^2)/(1-2sin^2) = (cos^2-2sin*cos+sin^2)/(1-2sin^2<BR>\n" );
document.write( "==================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );