document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=756302>Question 756302</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify each trig expression into 1 term: <BR>\n" );
document.write( "1.) sin(theta)+cos(theta)cot(theta)<BR>\n" );
document.write( "2.)cos^2(theta)+tan^2(theta)cos^2(theta)\r<BR>\n" );
document.write( "\n" );
document.write( "Verify each identity:<BR>\n" );
document.write( "3.) sec(theta)sin(theta)cot(theta)=1<BR>\n" );
document.write( "4.)csc^2(theta)-cot^2(theta)=1<BR>\n" );
document.write( "5.)sin^2(theta)<BR>\n" );
document.write( "   ------------<BR>\n" );
document.write( "    1-cos(theta)   = 1+cos(theta)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #460115 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=460115\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Simplify each trig expression into 1 term: <BR>\n" );
document.write( "1.) sin(theta)+cos(theta)cot(theta)<BR>\n" );
document.write( "----<BR>\n" );
document.write( "sin(x) + cos(x*(cos/sin)<BR>\n" );
document.write( "----<BR>\n" );
document.write( "= (sin^2(x) + cos^2(x))/sin(x) = 1/sin(x) = csc(x)<BR>\n" );
document.write( "=======================================================<BR>\n" );
document.write( "2.)cos^2(theta)+tan^2(theta)cos^2(theta)<BR>\n" );
document.write( "----<BR>\n" );
document.write( "cos^2(x) + [sin^2(x)/cos^2(x)*cos^2(x)]<BR>\n" );
document.write( "----<BR>\n" );
document.write( "= cos^2(x) + sin^2(x)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "= 1<BR>\n" );
document.write( "=======================================================<BR>\n" );
document.write( " <BR>\n" );
document.write( "Verify each identity:<BR>\n" );
document.write( "3.) sec(theta)sin(theta)cot(theta)=1<BR>\n" );
document.write( "(1/cos)*sin)(cos/sin) = 1<BR>\n" );
document.write( "Cancel all factors common to numerator and denominator:<BR>\n" );
document.write( "1 = 1<BR>\n" );
document.write( "========================<BR>\n" );
document.write( "4.)csc^2(theta)-cot^2(theta)=1<BR>\n" );
document.write( "(1/sin^2 - [cos^2/sin^2] = 1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "(1-cos^2)/sin^2 = 1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "sin^2/sin^2 = 1<BR>\n" );
document.write( "1 = 1<BR>\n" );
document.write( "========================<BR>\n" );
document.write( "5.) [sin^2(x)/(1-cos(x)] = (1+cos(x)<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "Cross-multiply to get:<BR>\n" );
document.write( "sin^2 = (1-cos)(1+cos)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "sin^2 = 1-cos^2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "sin^2 = sin^2<BR>\n" );
document.write( "======================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "=====================<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );