document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=711954>Question 711954</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the given expression in terms of x and y only. Simplify the result.\r<BR>\n" );
document.write( "\n" );
document.write( "tan(sin^-1x + cos^-1y)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #437825 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=437825\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write the given expression in terms of x and y only. Simplify the result. <BR>\n" );
document.write( "tan(sin^-1x + cos^-1y)<BR>\n" );
document.write( "notation: <BR>\n" );
document.write( "O=opposite side<BR>\n" );
document.write( "A=adjacent side<BR>\n" );
document.write( "H=hypotenuse<BR>\n" );
document.write( "..<BR>\n" );
document.write( "let angle a=sin^-1x<BR>\n" );
document.write( "sin a=x/1=0/H<BR>\n" );
document.write( "O=x, H=1<BR>\n" );
document.write( "A=(&#8730;(H^2-O^2)=&#8730;(1-x^2)<BR>\n" );
document.write( "tan a=O/A=x/&#8730;(1-x^2)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "let angle b=cos^-1y<BR>\n" );
document.write( "cos b=y/1=A/H<BR>\n" );
document.write( "A=y, H=1<BR>\n" );
document.write( "O=(&#8730;(H^2-A^2)=&#8730;(1-y^2)<BR>\n" );
document.write( "tan b=O/A=&#8730;(1-y^2)/y<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Identity:<BR>\n" );
document.write( "tan(a+b)=(tan a+tan b)/(1-tan a*tan b)<BR>\n" );
document.write( "=(x/&#8730;(1-x^2)+&#8730;(1-y^2)/y)/(1-x/&#8730;(1-x^2)*&#8730;(1-y^2)/y) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );