document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=799078>Question 799078</A>: <I><SPAN STYLE=\"word-break: break-all;\"> tan(sin^-1 3/4-cox^-1 1/7) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #482514 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=482514\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> My solution may not be elegant, but I think it's right.<BR>\n" );
document.write( "Given expression<BR>\n" );
document.write( "(1) tan(arcsin(3/4) - arccos(1/7))<BR>\n" );
document.write( "Let <BR>\n" );
document.write( "(2) a = arcsin(3/4), then<BR>\n" );
document.write( "(3) sin(a) = 3/4 and using<BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28a%29+%2B+cos%5E2%28a%29+=+1 ALIGN=MIDDLE  ALT=\"sin%5E2%28a%29+%2B+cos%5E2%28a%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get<BR>\n" );
document.write( "(5) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E2%28a%29+=+1+-+%283%2F4%29%5E2 ALIGN=MIDDLE  ALT=\"cos%5E2%28a%29+=+1+-+%283%2F4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "(6) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28a%29+=+sqrt%287%29%2F4 ALIGN=MIDDLE  ALT=\"cos%28a%29+=+sqrt%287%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now let<BR>\n" );
document.write( "(7) b = arccos(1/7), then<BR>\n" );
document.write( "(8) cos(b) = 1/7 and using<BR>\n" );
document.write( "(9) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28b%29+%2B+cos%5E2%28b%29+=+1 ALIGN=MIDDLE  ALT=\"sin%5E2%28b%29+%2B+cos%5E2%28b%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get<BR>\n" );
document.write( "(10)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin%5E2%28b%29+%2B+%281%2F7%29%5E2+=+1 ALIGN=MIDDLE  ALT=\"+sin%5E2%28b%29+%2B+%281%2F7%29%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "(11) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28b%29+=+1+-+%281%2F7%29%5E2 ALIGN=MIDDLE  ALT=\"sin%5E2%28b%29+=+1+-+%281%2F7%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or<BR>\n" );
document.write( "(12)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin%28b%29+=+%284%2F7%29%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"+sin%28b%29+=+%284%2F7%29%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now a biggy!<BR>\n" );
document.write( "Use the following identities<BR>\n" );
document.write( "(13) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28a-b%29+=+%28sin%28a-b%29%29%2F%28cos%28a-b%29%29 ALIGN=MIDDLE  ALT=\"tan%28a-b%29+=+%28sin%28a-b%29%29%2F%28cos%28a-b%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(14) sin(a-b) = sin(a)cos(b) - cos(a)sin(b)<BR>\n" );
document.write( "(15) cos(a-b) = cos(a)cos(b) + sin(a)sin(b) <BR>\n" );
document.write( "There may be a more direct way to get (13), but I dont have an extensive table of trig identities in my brain. These are the only ones I remember.<BR>\n" );
document.write( "Anyway substitute (3), (6), (8), and (12) into (14) and (15) to get<BR>\n" );
document.write( "(16)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sin%28a-b%29+=+%283%2F4%29%2A%281%2F7%29+-+%28sqrt%287%29%2F4%29%2A%284%2Asqrt%283%29%2F7%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "(17)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cos%28a-b%29+=+%28sqrt%287%29%2F4%29%2A%281%2F7%29+%2B+%283%2F4%29%2A%284%2Asqrt%283%29%2F7%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now put (16) and (17) into (13) to get the solution to the problem. Note that all four terms have the common denominator, 28. Since it is in a ratio, it cancels out to give us<BR>\n" );
document.write( "(18)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28arcsin%283%2F4%29+-+arccos%281%2F7%29%29+=+%283+-+4%2Asqrt%287%29%2Asqrt%283%29%29%2F%28sqrt%287%29+%2B+3%2A4%2Asqrt%283%29%29++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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