document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=826147>Question 826147</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If x = r sin A cos B and y = r sin A sin B and z = r cos A ,verify x^2 + y^2 + z^2 = r^2. <BR>\n" );
document.write( "Can you please help me?Thanks so much in advance:) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #497951 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=497951\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What we're going to do is take:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2+%2B+z%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2+%2B+z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and substitute in the given expressions for x, y and z. Then we will use algebra and/or trig properties to transform the expression into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2 ALIGN=MIDDLE  ALT=\"r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "Substituting in the given expressions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%2Asin%28A%29%2Acos%28B%29%29%5E2+%2B+%28r%2Asin%28A%29%2Asin%28B%29%29%5E2%2B%28r%2Acos%28A%29%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Squaring each expression:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2%2Asin%5E2%28A%29%2Acos%5E2%28B%29+%2B+r%5E2%2Asin%5E2%28A%29%2Asin%5E2%28B%29%2Br%5E2%2Acos%5E2%28A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2 ALIGN=MIDDLE  ALT=\"r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2%28sin%5E2%28A%29%2Acos%5E2%28B%29+%2B+sin%5E2%28A%29%2Asin%5E2%28B%29%2Bcos%5E2%28A%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, if we can find a way to turn the second factor into a 1, we will be finished! Factoring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28A%29 ALIGN=MIDDLE  ALT=\"sin%5E2%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > out of the first two terms in the second factor:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2%28sin%5E2%28A%29%28cos%5E2%28B%29+%2B+sin%5E2%28B%29%29%2Bcos%5E2%28A%29%29 ALIGN=MIDDLE  ALT=\"r%5E2%28sin%5E2%28A%29%28cos%5E2%28B%29+%2B+sin%5E2%28B%29%29%2Bcos%5E2%28A%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%5E2%28B%29+%2B+sin%5E2%28B%29+=+1 ALIGN=MIDDLE  ALT=\"cos%5E2%28B%29+%2B+sin%5E2%28B%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2%28sin%5E2%28A%29%2Bcos%5E2%28A%29%29 ALIGN=MIDDLE  ALT=\"r%5E2%28sin%5E2%28A%29%2Bcos%5E2%28A%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since <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;\" > this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2 ALIGN=MIDDLE  ALT=\"r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );