Miscelánea Trigonometría (1)

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=2 height=24 BGCOLOR="#003366" TEXT="#F7F7FF"> <div> <FONT SIZE="4" COLOR="#00FFCC" FACE="Bell MT" ><B>P r e c á l c u l o 21</B><B> | </B></FONT><A HREF="index.htm" TARGET="_top" TITLE="Precálculo21"><U><B>Página principal</B></U></A><B> </B><FONT SIZE="4" COLOR="#00FFCC" FACE="Bell MT" ><B> |  </B></FONT><A HREF="id418.htm" TARGET="_top" TITLE="_"><U><B>Contenido</B></U></A><B>  </B><FONT SIZE="4" COLOR="#00FFCC" FACE="Bell MT" ><B>|</B></FONT><B> </B><A HREF="id507.htm" TARGET="_top" TITLE="Misceláneas"><U><B> Misceláneas</B></U></A><B>  |</B></div> <DIV ALIGN="LEFT"></DIV> <div> </div> </td> </tr><tr> <td valign="top" width=160 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <B> <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:160px;height:600px" data-ad-client="ca-pub-6266400581769473" data-ad-slot="5543838917"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </B></div> </td> <td valign="top" height=456 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <B>Miscelánea Trigonometría (1)</B></div> <bR> <div>  <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:728px;height:90px" data-ad-client="ca-pub-6266400581769473" data-ad-slot="9294650114"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </div> <bR> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="748" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 171 ><NOBR><div> <A HREF="#1_1" TITLE="Miscelánea Trigonometría (1)"><U><IMG SRC="fe6eda30.gif" border=0 width="237" height="163" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><IMG SRC="fe7c89f0.gif" border=0 width="200" height="159" ALT="Imagen de mapa de bits" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> <tD VALIGN=TOP COLSPAN=2><NOBR><div> <A HREF="#2" TITLE="Miscelánea Trigonometría (1)"><U><IMG SRC="102df33d0.gif" border=0 width="243" height="61" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <A HREF="#3__" TITLE="Miscelánea Trigonometría (1)"><U><B><IMG SRC="103d143d0.gif" border=0 width="276" height="61" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 144 ><NOBR><div> <A HREF="#4" TITLE="Miscelánea Trigonometría (1)"><U><B><IMG SRC="103e6d2b0.gif" border=0 width="365" height="43" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></U></A></div> </NOBR></tD> <tD VALIGN=TOP COLSPAN=2><NOBR><div> <A HREF="#5_" TITLE="Miscelánea Trigonometría (1)"><U><IMG SRC="104e0d880.gif" border=0 width="269" height="136" ALT="Imagen de mapa de bits" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 94 WIDTH="448"><div> <A HREF="#6" TITLE="Miscelánea Trigonometría (1)"><U><B><IMG SRC="1050cf290.gif" border=0 width="207" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></U></A><B>            </B><A HREF="#7" TITLE="Miscelánea Trigonometría (1)"><U><B><IMG SRC="1051bd290.gif" border=0 width="189" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></U></A></div> </tD> <tD VALIGN=TOP COLSPAN=2><NOBR><div> <A HREF="#8" TITLE="Miscelánea Trigonometría (1)"><U><IMG SRC="106309300.gif" border=0 width="265" height="48" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=3 HEIGHT= 139 ><NOBR><div> Demuestre las siguientes identidades:</div> <bR> <div> <A HREF="#9" TITLE="Miscelánea Trigonometría (1)"><U><IMG SRC="10660b290.gif" border=0 width="267" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>              <A HREF="#10" TITLE="Miscelánea Trigonometría (1)"><U><IMG SRC="1069f32c0.gif" border=0 width="243" height="44" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <bR> <div> <A HREF="#11" TITLE="Miscelánea Trigonometría (1)"><U><IMG SRC="106c1b150.gif" border=0 width="283" height="21" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 93 ><NOBR><div> <A HREF="#12" TITLE="Miscelánea Trigonometría (1)"><U><IMG SRC="106f63180.gif" border=0 width="355" height="24" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP COLSPAN=2><NOBR><div> <A HREF="#13" TITLE="Miscelánea Trigonometría (1)"><U><IMG SRC="108a00550.gif" border=0 width="256" height="85" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=3 HEIGHT= 49 ><NOBR><div> <A HREF="#14_" TITLE="Miscelánea Trigonometría (1)"><U><IMG SRC="109114290.gif" border=0 width="532" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> </tR> </TABLE></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <B>S o l u c i o n e s </B></div> <bR> <div>  <A NAME="1_1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="4" COLOR="#CC0033" FACE="Georgia" ><B><IMG SRC="105255170.gif" border=0 width="85" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></FONT></div> <div> <B> <TABLE BORDER="0" CELLPADDING="2" CELLSPACING="1" WIDTH="733" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 635 ><NOBR><div> <IMG SRC="fea05270.gif" border=0 width="517" height="551" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <IMG SRC="fe8c89f0.gif" border=0 width="200" height="159" ALT="Imagen de mapa de bits" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div> <IMG SRC="fe9a7bb0.gif" border=0 width="167" height="443" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> </TABLE></B></div> <bR> <div> <B> <A NAME="2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="102e55170.gif" border=0 width="85" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="102f74d80.gif" border=0 width="628" height="472" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="3__"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B>3.  </B><FONT SIZE="4" COLOR="#000000" FACE="Georgia" ><U>Solución</U>:</FONT></div> <div> <TABLE BORDER="0" CELLPADDING="2" CELLSPACING="1" WIDTH="721" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 197 ><NOBR><div> <IMG SRC="1033c5bd0.gif" border=0 width="453" height="189" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <IMG SRC="1032faaf0.gif" border=0 width="250" height="175" ALT="Imagen de mapa de bits" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=2 HEIGHT= 1660 ><NOBR><div> <IMG SRC="10345d5b0.gif" border=0 width="605" height="347" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div> <B> <A NAME="4"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B>4.  </B><FONT SIZE="4" COLOR="#000000" FACE="Georgia" ><U>Solución</U>:</FONT></div> <div> <IMG SRC="103f559b0.gif" border=0 width="597" height="155" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div> <B> <A NAME="5_"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B>5.  </B><FONT SIZE="4" COLOR="#000000" FACE="Georgia" ><U>Solución</U>:</FONT></div> <div> <IMG SRC="104f4bb30.gif" border=0 width="587" height="435" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div> <B> <A NAME="6"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="105355170.gif" border=0 width="85" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="105455470.gif" border=0 width="597" height="327" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="7"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="105555170.gif" border=0 width="85" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="1056a1c00.gif" border=0 width="673" height="192" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> </NOBR></tD> </tR> </TABLE></div> <bR> <div> <B> <A NAME="8"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="106455170.gif" border=0 width="85" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="1065f3980.gif" border=0 width="499" height="152" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="9"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="106855170.gif" border=0 width="85" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="106785fb0.gif" border=0 width="389" height="251" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="10"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="106a5f170.gif" border=0 width="95" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="106bbd190.gif" border=0 width="445" height="281" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="11"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="106d5f170.gif" border=0 width="95" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="106e9b230.gif" border=0 width="411" height="291" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="12"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="10705f170.gif" border=0 width="95" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="1071948b0.gif" border=0 width="660" height="139" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="13"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B><IMG SRC="10875f170.gif" border=0 width="95" height="23" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B> <TABLE BORDER="0" CELLPADDING="1" CELLSPACING="1" WIDTH="705" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 151 ><NOBR><div> <IMG SRC="108bab8f0.gif" border=0 width="427" height="143" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <IMG SRC="109dcf7e0.gif" border=0 width="207" height="126" ALT="Imagen de mapa de bits" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> </TABLE></B></div> <div> <B><IMG SRC="108c27b80.gif" border=0 width="551" height="184" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> <div> <B> <A NAME="14_"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A></B><B>14.  </B><FONT SIZE="4" COLOR="#000000" FACE="Georgia" ><U>Solución</U>:</FONT></div> <div> <B><IMG SRC="1092ed710.gif" border=0 width="749" height="369" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <bR> </td> </tr></table></body>