document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176724>Question 1176724</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If x > 0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+arcsin+%28+x%2F2+%29+%2B+arccos+%28+x%2F2+%29+%29+%2F+arctan+%28+x+%29+=+3%2F2+ ALIGN=MIDDLE  ALT=\"+%28+arcsin+%28+x%2F2+%29+%2B+arccos+%28+x%2F2+%29+%29+%2F+arctan+%28+x+%29+=+3%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, solve for x. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #804169 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=804169\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
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document.write( "Added after seeing the response from tutor @ikleyn....<br><BR>\n" );
document.write( "She used a nice fact that I overlooked that makes solving this problem relatively easy.<br><BR>\n" );
document.write( "The numerator is the sum of two angles, each less than pi/2 or 90 degrees, in which the sine of one angle is the cosine of the other.  But that makes the two angles complementary, so the numerator of the fraction is just pi/2 (radians), or 90 degrees.<br><BR>\n" );
document.write( "Then from there the solution is relatively easy.<br><BR>\n" );
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document.write( "To solve this algebraically, I think you would have to use calculus and the Taylor series expressions for arcsin, arccos, and arctan.  And even then solving the problem would probably involve very ugly calculations.<br><BR>\n" );
document.write( "On the other hand, solving the problem using a graphing calculator is easy -- simply graph the expressions on the two sides of the equation and find where they are equal.<br><BR>\n" );
document.write( "Note that the domains of arcsin and arctan are from -pi/2 to pi/2 and the domain of arccos is from 0 to pi; so the domain of the expression shown is from 0 to pi/2.<br><BR>\n" );
document.write( "HOWEVER....<br><BR>\n" );
document.write( "The topic you have chosen for your post is trigonometry basics -- and solving the problem either of those ways is not basics.<br><BR>\n" );
document.write( "If solving the problem involves basic trigonometry, then the answer likely lies with one of the \"nice\" acute angles.  And for \"nice\" acute angles, with the \"x/2\" as the argument for the sine and cosine and \"x\" as the argument for tangent, x=sqrt(3) seems a likely candidate.<br><BR>\n" );
document.write( "And, indeed, with the angles in degrees,<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=arcsin%28sqrt%283%29%2F2%29+=+60 ALIGN=MIDDLE  ALT=\"arcsin%28sqrt%283%29%2F2%29+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=arccos%28sqrt%283%29%2F2%29+=+30 ALIGN=MIDDLE  ALT=\"arccos%28sqrt%283%29%2F2%29+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=arctan%28sqrt%283%29%29+=+60 ALIGN=MIDDLE  ALT=\"arctan%28sqrt%283%29%29+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "and<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28arcsin%28sqrt%283%29%2F2%29%2Barccos%28sqrt%283%29%2F2%29%29%2Farctan%28sqrt%283%29%29+=+%2860%2B30%29%2F60+=+3%2F2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: x = sqrt(3)<br><BR>\n" );
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