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 #185540 by </B><A HREF=/tutors/aboutme.mpl?userid=Greenfinch><B>Greenfinch(383)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Greenfinch><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=Greenfinch><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=185540\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have the right start. <BR>\n" );
document.write( "(sinx cosy  + sinycosx)(sinxcosy - sinycosx) which is difference of 2 squares so<BR>\n" );
document.write( "(sin^2 x cos^2 y)- (sin^2 y cos^2 x) when multiplied out<BR>\n" );
document.write( "Now sin^2 = 1 - cos^2 so, rewriting<BR>\n" );
document.write( "cos^2 y ( 1 - cos^2 x) - cos^2 x (1 - cos^2 y) and expanding<BR>\n" );
document.write( "cos^2 y - cos^2 y cos^2 x - cos^2 x + cos^2 x cos^2 y then adding up<BR>\n" );
document.write( "cos^2 y - cos^2 x </SPAN>\n" );
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