document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=352159>Question 352159</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that cos(x)-sin(x)cot(x)=0 and <BR>\n" );
document.write( "tan^5(x)=tan^3(x)sec^3(x)-tan^3(x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #251690 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=251690\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Prove that cos(x)-sin(x)cot(x)=0 and <BR>\n" );
document.write( "tan^5(x)=tan^3(x)sec^3(x)-tan^3(x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "sohcahtoa<BR>\n" );
document.write( "sin = opp/hyp, cos = adj/hyp, tan = opp/adj<BR>\n" );
document.write( "adj, opp, hyp sides of a right triangle<BR>\n" );
document.write( "tan = sin/cos, cot = 1/tan = cos/sin<BR>\n" );
document.write( "sec = 1/cos, csc = 1/sin<BR>\n" );
document.write( "sin^2 + cos^2 = 1 (Pythagorean Identity)<BR>\n" );
document.write( "sin^2/cos^2 + 1 = 1/cos^2 = tan^2 + 1 = sec^2 (Pythagorean Identity)<BR>\n" );
document.write( "1 + cos^2/sin^2 = 1/sin^2 = 1 + cot^2 = csc^2 (Pythagorean Identity)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "cos(x) - sin(x)cot(x) = 0, prove<BR>\n" );
document.write( "cos(x) - sin(x) * cos(x)/sin(x) = 0, prove (replaced cot(x))<BR>\n" );
document.write( "cos(x) - cos(x) = 0, true\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "tan^5(x) = tan^3(x)sec^3(x) - tan^3(x), prove<BR>\n" );
document.write( "tan^5(x) = tan^3(x)(sec^3(x) - 1), prove\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "sec^2 - 1 = tan^2, NOT sec^3 - 1, the exponent on the sec^3(x) is wrong<BR>\n" );
document.write( "the exponent on the sec^3(x) should be a 2 making it sec^2(x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when corrected:<BR>\n" );
document.write( "tan^5(x) = tan^3(x)(sec^2(x) - 1), prove<BR>\n" );
document.write( "tan^5(x) = tan^3(x)(tan^2(x)), prove<BR>\n" );
document.write( "tan^5(x) = tan^5(x), true\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );