document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=627391>Question 627391</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use an algebraic method to find the exact solution(s) for sin 2x = sin x, where 0 is less than or equal to x which is less than 2 pie (Please show work) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #394911 by </B><A HREF=/tutors/aboutme.mpl?userid=hammy><B>hammy(9)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=hammy><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=hammy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=394911\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sin 2x=sin x<BR>\n" );
document.write( "sin(x+y)=sinx*cosy+siny*cosx<BR>\n" );
document.write( "so, sin 2x or sin(x+x)=2sinxcosx<BR>\n" );
document.write( "Substitute<BR>\n" );
document.write( "2sinxcosx=sinx<BR>\n" );
document.write( "2sinxcosx-sinx=0<BR>\n" );
document.write( "sinx(2cosx-1)=0<BR>\n" );
document.write( "By the zero product property<BR>\n" );
document.write( "sinx=0   and   2cosx-1=0\r<BR>\n" );
document.write( "\n" );
document.write( "sinx=0 when x=0,pie\r<BR>\n" );
document.write( "\n" );
document.write( "2cosx-1=0<BR>\n" );
document.write( "2cosx=1<BR>\n" );
document.write( "cosx=1/2 when x=pie/3,5*pie/3 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );