document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191003>Question 1191003</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that : cos(72°) =(1/2)sqrt(4sin²(36°)-1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822775 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=822775\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Prove that : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%2872%29+=%281%2F2%29sqrt%284sin%5E2%2836%29-1%29 ALIGN=MIDDLE  ALT=\"cos%2872%29+=%281%2F2%29sqrt%284sin%5E2%2836%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solve left side:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%2872%29 ALIGN=MIDDLE  ALT=\"cos+%2872%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .....use identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28+72%29++=cos+%2890+-+18%29 ALIGN=MIDDLE  ALT=\"cos%28+72%29++=cos+%2890+-+18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >°\r<BR>\n" );
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document.write( "use identity\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28a-b%29=sin%28a%29+sin%28b%29+%2B+cos%28a%29+cos%28b%29 ALIGN=MIDDLE  ALT=\"cos%28a-b%29=sin%28a%29+sin%28b%29+%2B+cos%28a%29+cos%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >........where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=90 ALIGN=MIDDLE  ALT=\"a=90\"   DISABLED_style= \"max-width:90%; height:auto;\" >° and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=18 ALIGN=MIDDLE  ALT=\"b=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >°\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%2890+-+18%29+=sin%2890%29+sin%2818%29+%2B+cos%2890%29+cos%2818%29 ALIGN=MIDDLE  ALT=\"cos+%2890+-+18%29+=sin%2890%29+sin%2818%29+%2B+cos%2890%29+cos%2818%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cos+%2890+-+18%29+=1%2A+sin%2818%29+%2B+0%2Acos%2818%29 ALIGN=MIDDLE  ALT=\"+cos+%2890+-+18%29+=1%2A+sin%2818%29+%2B+0%2Acos%2818%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%2890+-+18%29+=+sin%2818%29+ ALIGN=MIDDLE  ALT=\"cos+%2890+-+18%29+=+sin%2818%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos+%2890+-+18%29+=%281%2F4%29+%28sqrt%285%29+-+1%29 ALIGN=MIDDLE  ALT=\"cos+%2890+-+18%29+=%281%2F4%29+%28sqrt%285%29+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " \r<BR>\n" );
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document.write( "solve right side:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29sqrt%284sin%5E2%2836%29-1%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29sqrt%284sin%5E2%2836%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%2836%29=5%2F8+-+sqrt%285%29%2F8 ALIGN=MIDDLE  ALT=\"sin%5E2%2836%29=5%2F8+-+sqrt%285%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29sqrt%284+%285%2F8+-+sqrt%285%29%2F8%29+-+1%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29sqrt%284+%285%2F8+-+sqrt%285%29%2F8%29+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29sqrt%28%281%2F2%29+%283+-+sqrt%285%29%29%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29sqrt%28%281%2F2%29+%283+-+sqrt%285%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%28sqrt%285%29%2F2+-+1%2F2%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%28sqrt%285%29%2F2+-+1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%28sqrt%285%29+-+1%29 ALIGN=MIDDLE  ALT=\"%281%2F4%29%28sqrt%285%29+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, both sides have same answer\r<BR>\n" );
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document.write( "then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%2872%29+=%281%2F2%29sqrt%284sin%5E2%2836%29-1%29 ALIGN=MIDDLE  ALT=\"cos%2872%29+=%281%2F2%29sqrt%284sin%5E2%2836%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%28sqrt%285%29+-+1%29=%281%2F4%29%28sqrt%285%29+-+1%29 ALIGN=MIDDLE  ALT=\"%281%2F4%29%28sqrt%285%29+-+1%29=%281%2F4%29%28sqrt%285%29+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ->proven\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );