document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=769293>Question 769293</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the expression below, write an equivalent expression that involves x only. Assume x is positive.<BR>\n" );
document.write( "csc(sin^-1(1/x)) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #468766 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=468766\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
document.write( "(1) csc(y) = csc(arcsin(1/x)), where I use the equivalent notation arcsin(z) = sin^(-1)z. Comparing the left side to the right side we see that<BR>\n" );
document.write( "(2) y = arcsin(1/x) or<BR>\n" );
document.write( "(3) sin(y) = 1/x<BR>\n" );
document.write( "Now use the identity<BR>\n" );
document.write( "(4) csc(y) = 1/sin(y) and (3) we get<BR>\n" );
document.write( "(5) csc(y) = 1/(1/x) or<BR>\n" );
document.write( "(6) csc(y) = x <BR>\n" );
document.write( "Answer: csc(arcsin(1/x) = x </SPAN>\n" );
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