document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170774>Question 1170774</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to prove <BR>\n" );
document.write( "1.sinθ = cosθ tanθ<BR>\n" );
document.write( "2. 1/cosθ=tanθ/sinθ\r<BR>\n" );
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document.write( "3. cos2 θ tan2 θ = sin2 θ<BR>\n" );
document.write( "4. sinθtanθ + cosθ =1/cosθ\r<BR>\n" );
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document.write( "5. sinθ(1 + tanθ) = tanθ(sinθ + cosθ) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #795665 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=795665\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How to prove\r<BR>\n" );
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document.write( "1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29+=+cos%28theta%29%2Atan%28theta%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29+=+cos%28theta%29%2Atan%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "start with right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28theta%29%2Atan%28theta%29 ALIGN=MIDDLE  ALT=\"cos%28theta%29%2Atan%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........use identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29=sin%28theta%29%2Fcos%28theta%29 ALIGN=MIDDLE  ALT=\"tan%28theta%29=sin%28theta%29%2Fcos%28theta%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%28theta%29%28sin%28theta%29%2Fcos%28theta%29%29 ALIGN=MIDDLE  ALT=\"cos%28theta%29%28sin%28theta%29%2Fcos%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........simplify\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28cos%28theta%29+%29%28sin%28theta%29%2Fcross%28cos%28theta%29%29%29 ALIGN=MIDDLE  ALT=\"cross%28cos%28theta%29+%29%28sin%28theta%29%2Fcross%28cos%28theta%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=sin%28theta%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fcos%28theta%29=tan%28theta%29%2Fsin%28theta%29 ALIGN=MIDDLE  ALT=\"1%2Fcos%28theta%29=tan%28theta%29%2Fsin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "start with right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29%2Fsin%28theta%29 ALIGN=MIDDLE  ALT=\"tan%28theta%29%2Fsin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........use identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29=sin%28theta%29%2Fcos%28theta%29 ALIGN=MIDDLE  ALT=\"tan%28theta%29=sin%28theta%29%2Fcos%28theta%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=%28sin%28theta%29%2Fcos%28theta%29%29%2Fsin%28theta%29 ALIGN=MIDDLE  ALT=\"%28sin%28theta%29%2Fcos%28theta%29%29%2Fsin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29%2F%28cos%28theta%29%2Asin%28theta%29%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29%2F%28cos%28theta%29%2Asin%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28sin%28theta%29%291%2F%28cos%28theta%29%2Across%28sin%28theta%29%29%29 ALIGN=MIDDLE  ALT=\"cross%28sin%28theta%29%291%2F%28cos%28theta%29%2Across%28sin%28theta%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=1%2Fcos%28theta%29 ALIGN=MIDDLE  ALT=\"1%2Fcos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "3. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282theta%29+tan%282theta%29=+sin%282theta%29 ALIGN=MIDDLE  ALT=\"cos%282theta%29+tan%282theta%29=+sin%282theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "start with left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282theta%29+tan%282theta%29 ALIGN=MIDDLE  ALT=\"cos%282theta%29+tan%282theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........use identities <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282theta%29=cos%5E2%28theta%29+-+sin%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"cos%282theta%29=cos%5E2%28theta%29+-+sin%5E2%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%282theta%29=+sin%282theta%29%2Fcos%282theta%29 ALIGN=MIDDLE  ALT=\"tan%282theta%29=+sin%282theta%29%2Fcos%282theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cos%5E2%28theta%29+-+sin%5E2%28theta%29%29%28sin%282theta%29%2Fcos%282theta%29%29 ALIGN=MIDDLE  ALT=\"%28cos%5E2%28theta%29+-+sin%5E2%28theta%29%29%28sin%282theta%29%2Fcos%282theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >....use  again <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%282theta%29=cos%5E2%28theta%29+-+sin%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"cos%282theta%29=cos%5E2%28theta%29+-+sin%5E2%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cos%5E2%28theta%29+-+sin%5E2%28theta%29%29%28sin%282theta%29%2F%28cos%5E2%28theta%29+-+sin%5E2%28theta%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%28cos%5E2%28theta%29+-+sin%5E2%28theta%29%29%29%28sin%282theta%29%2F%28cross%28cos%5E2%28theta%29+-+sin%5E2%28theta%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%282theta%29 ALIGN=MIDDLE  ALT=\"sin%282theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "4. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29tan%28theta%29+%2B+cos%28theta%29+=1%2Fcos%28theta%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29tan%28theta%29+%2B+cos%28theta%29+=1%2Fcos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "start with left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29tan%28theta%29+%2B+cos%28theta%29+ ALIGN=MIDDLE  ALT=\"sin%28theta%29tan%28theta%29+%2B+cos%28theta%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....use identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29=sin%28theta%29%2Fcos%28theta%29 ALIGN=MIDDLE  ALT=\"tan%28theta%29=sin%28theta%29%2Fcos%28theta%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=sin%28theta%29%28sin%28theta%29%2Fcos%28theta%29%29+%2B+cos%28theta%29+ ALIGN=MIDDLE  ALT=\"sin%28theta%29%28sin%28theta%29%2Fcos%28theta%29%29+%2B+cos%28theta%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=sin%5E2%28theta%29%2Fcos%28theta%29+%2B+cos%28theta%29 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29%2Fcos%28theta%29+%2B+cos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ....use identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28theta%29=1-cos%5E2%28theta%29 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29=1-cos%5E2%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-cos%5E2%28theta%29%29%2Fcos%28theta%29+%2B+cos%28theta%29+ ALIGN=MIDDLE  ALT=\"%281-cos%5E2%28theta%29%29%2Fcos%28theta%29+%2B+cos%28theta%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-cos%5E2%28theta%29%29%2Fcos%28theta%29+%2B+cos%5E2%28theta%29%2Fcos%28theta%29+ ALIGN=MIDDLE  ALT=\"%281-cos%5E2%28theta%29%29%2Fcos%28theta%29+%2B+cos%5E2%28theta%29%2Fcos%28theta%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-cos%5E2%28theta%29+%2B+cos%5E2%28theta%29%29%2Fcos%28theta%29+ ALIGN=MIDDLE  ALT=\"%281-cos%5E2%28theta%29+%2B+cos%5E2%28theta%29%29%2Fcos%28theta%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-cross%28cos%5E2%28theta%29%29+%2Bcross%28+cos%5E2%28theta%29%29%29%2Fcos%28theta%29+ ALIGN=MIDDLE  ALT=\"%281-cross%28cos%5E2%28theta%29%29+%2Bcross%28+cos%5E2%28theta%29%29%29%2Fcos%28theta%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fcos%28theta%29+ ALIGN=MIDDLE  ALT=\"1%2Fcos%28theta%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "5. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29+%281+%2B+tan%28theta%29+%29+=+tan%28theta%29+%28sin%28theta%29++%2B+cos%28theta%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "start with left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29+%281+%2B+tan%28theta%29+%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29+%281+%2B+tan%28theta%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ....use identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29=sin%28theta%29%2Fcos%28theta%29 ALIGN=MIDDLE  ALT=\"tan%28theta%29=sin%28theta%29%2Fcos%28theta%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=sin%28theta%29+%281+%2B+sin%28theta%29%2Fcos%28theta%29+%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29+%281+%2B+sin%28theta%29%2Fcos%28theta%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=sin%28theta%29+%28cos%28theta%29+%2Fcos%28theta%29+%2B+sin%28theta%29%2Fcos%28theta%29+%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29+%28cos%28theta%29+%2Fcos%28theta%29+%2B+sin%28theta%29%2Fcos%28theta%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=sin%28theta%29+%28%28cos%28theta%29+%2B+sin%28theta%29%29%2Fcos%28theta%29+%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29+%28%28cos%28theta%29+%2B+sin%28theta%29%29%2Fcos%28theta%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >....factor out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fcos%28theta%29+ ALIGN=MIDDLE  ALT=\"1%2Fcos%28theta%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=sin%28theta%29%281%2Fcos%28theta%29+%29+%28cos%28theta%29+%2B+sin%28theta%29%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29%281%2Fcos%28theta%29+%29+%28cos%28theta%29+%2B+sin%28theta%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=%28sin%28theta%29%2Fcos%28theta%29+%29+%28cos%28theta%29+%2B+sin%28theta%29%29 ALIGN=MIDDLE  ALT=\"%28sin%28theta%29%2Fcos%28theta%29+%29+%28cos%28theta%29+%2B+sin%28theta%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=tan%28theta%29++%28cos%28theta%29+%2B+sin%28theta%29%29 ALIGN=MIDDLE  ALT=\"tan%28theta%29++%28cos%28theta%29+%2B+sin%28theta%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );