document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=735516>Question 735516</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a) prove that (1+tan A + sec A)(1+cot A-cosecA)=2<BR>\n" );
document.write( "b) Prove that Sin 20degree.sin40degree.sin 60degree.Sin80degree = 3/16<BR>\n" );
document.write( "c) sin 5A+2sin7A+sin9A/Cos3A+2cos5A+Cos7A = Sin2A+Cos2A.Tan5A<BR>\n" );
document.write( "d) Show that Sin112+Cos12 / Cos12-Sin12 = Cot35<BR>\n" );
document.write( "e) Prove that Sin 7x+Sinx / Cos5x-Cos3x = Sin2x-Cos2x.cotx<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #449461 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=449461\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) prove that (1+tan A + sec A)(1+cot A-cosecA)=2\r<BR>\n" );
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document.write( "LHS =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281+%2B+%28sin+A%2Fcos+A%29%2B%281%2Fcos+A%29%29%281%2B%28cos+A%2Fsin+A%29-%281%2Fsin+A%29%29 ALIGN=MIDDLE   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=+%28%28+cos+A+%2B+sin+A+%2B1%29%2Fcos+A%29%28%28sin+A+%2Bcos+A+-1%29%2Fsin+A%29 ALIGN=MIDDLE  ALT=\"+%28%28+cos+A+%2B+sin+A+%2B1%29%2Fcos+A%29%28%28sin+A+%2Bcos+A+-1%29%2Fsin+A%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=+%28%28cos+A+%2Bsin+A+%29%5E2+-1%29%2Fsin+A+cos+A ALIGN=MIDDLE  ALT=\"+%28%28cos+A+%2Bsin+A+%29%5E2+-1%29%2Fsin+A+cos+A\"   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=%28+cos%5E2+%28A+%29%2Bsin+%5E2%28+A%29+%2B2%2Asin+A+cos+A+-1%29%2F%28sin+A+cos+A%29 ALIGN=MIDDLE  ALT=\"%28+cos%5E2+%28A+%29%2Bsin+%5E2%28+A%29+%2B2%2Asin+A+cos+A+-1%29%2F%28sin+A+cos+A%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%2B2+sin+A+cosA-1%29%2Fsin+A+cos+A ALIGN=MIDDLE  ALT=\"%281%2B2+sin+A+cosA-1%29%2Fsin+A+cos+A\"   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( "LHS = RHS\r<BR>\n" );
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document.write( "b) Prove that Sin 20degree.sin40degree.sin 60degree.Sin80degree = 3/16\r<BR>\n" );
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document.write( " sin(A+B) = sin A cos B + cos A sin B\r<BR>\n" );
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document.write( "sin(40) as sin(60-20)<BR>\n" );
document.write( "sin(80) as sin(60+20)<BR>\n" );
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document.write( " sin(20)•sin(60-20)•[&#8730;(3)/2]•sin(60+20)\r<BR>\n" );
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document.write( "- Simplify sin(60-20)•sin(60+20)<BR>\n" );
document.write( " sin(60-20) = sin60•cos20 - sin20•cos60<BR>\n" );
document.write( " sin(60+20)= sin60•cos20 + sin20•cos60<BR>\n" );
document.write( " multiply <BR>\n" );
document.write( " = sin²60•cos²20 - sin²20•cos²60\r<BR>\n" );
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document.write( "cos²A = 1 - sin²A\r<BR>\n" );
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document.write( "sin²60•cos²20 - sin²20•cos²60<BR>\n" );
document.write( " = sin²60•(1-sin²20) - sin²20•(1-sin²60)<BR>\n" );
document.write( " = sin²60- sin²20•sin²60 - sin²20 + sin²20•sin²60<BR>\n" );
document.write( " = sin²60 - sin²20<BR>\n" );
document.write( " = 3/4 - sin²20\r<BR>\n" );
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document.write( " We get<BR>\n" );
document.write( " = sin20•[&#8730;(3)/2]•(3/4 - sin²20)<BR>\n" );
document.write( " = [&#8730;(3)/8]•(3sin20 - 4sin³20)\r<BR>\n" );
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document.write( " we know that<BR>\n" );
document.write( " sin(3A) = 3sin(A) - 4sin³(A)<BR>\n" );
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document.write( "(3sin20 - 4sin³20) = sin60\r<BR>\n" );
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document.write( "we have<BR>\n" );
document.write( " = [&#8730;(3)/8]•sin60<BR>\n" );
document.write( " = [&#8730;(3)/8]•[&#8730;(3)/2)<BR>\n" );
document.write( " = 3/16\r<BR>\n" );
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document.write( "LHS = RHS\r<BR>\n" );
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document.write( " </SPAN>\n" );
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