document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=253255>Question 253255</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please help me prove that sin(x+y)sin(x-y)=cos^2y-cos^2x? \r<BR>\n" );
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document.write( "This is what I have done so far...\r<BR>\n" );
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document.write( "sin(x+y)sin(x-y)can be changed to(sinxcosy+sinycosx)(sinxcosy-sinycosx) \r<BR>\n" );
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document.write( "Also, cos^2y-cos^2x can be changed to 1-sin^y-1-sin^2x\r<BR>\n" );
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document.write( "I'm not sure if I am going about this the right way, so if not, could you please point me in the right direction? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #185530 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=185530\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We have to prove:<BR>\n" );
document.write( "(i) sin(x+y)*sin(x-y))=(cos^2y-cos^2x<BR>\n" );
document.write( "I will simplify the left into the right.<BR>\n" );
document.write( "identity: sin (x+y) = sinxcosy + sinycosx<BR>\n" );
document.write( "identity: sin(x-y) = sinxcosy - sinycosx <BR>\n" );
document.write( "from (i) we get<BR>\n" );
document.write( "(ii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sinxcosy+%2B+sinycosx%29%2A%28sinxcosy+-+sinycosx%29 ALIGN=MIDDLE  ALT=\"%28sinxcosy+%2B+sinycosx%29%2A%28sinxcosy+-+sinycosx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply and we get<BR>\n" );
document.write( "(iii) sin^2x*cos^2y - sin^2y*cos^2x<BR>\n" );
document.write( "identity: sin^2x = 1 - cos^2x<BR>\n" );
document.write( "identity: sin^2y = 1 - cos^2y<BR>\n" );
document.write( "(iii) becomes<BR>\n" );
document.write( "(iv) (1-cos^2x)(cos^2y) - (1-cos^2y)(cos^2x)<BR>\n" );
document.write( "simplifying (iv) we get<BR>\n" );
document.write( "(v) cos^2y - cos^2x<BR>\n" );
document.write( "QED </SPAN>\n" );
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