document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=138819>Question 138819</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove the identity: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28a+%2B+B%29+sin+%28a-B%29+=+%28sin%28a%29%29%5E2-%28sin%28B%29%29%5E2 ALIGN=MIDDLE  ALT=\"sin%28a+%2B+B%29+sin+%28a-B%29+=+%28sin%28a%29%29%5E2-%28sin%28B%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (x is theta) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #101275 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=101275\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note: I'm only manipulating the left side. I'm not touching the right side. I'm only showing it for comparison.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin\left(a+B\right)\sin\left(a-B\right)=\sin^2\left(a\right)-\sin^2\left(B\right)\"> Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(\sin\left(a\right)\cos\left(B\right)+\cos\left(a\right)\sin\left(B\right)\right)\left(\sin\left(a\right)\cos\left(B\right)-\cos\left(a\right)\sin\left(B\right)\right)=\sin^2\left(a\right)-\sin^2\left(B\right)\"> Expand by using the Sum-Difference Formulas\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin^2\left(a\right)\cos^2\left(B\right)-\sin\left(a\right)\cos\left(a\right)\sin\left(B\right)\cos\left(B\right)+\sin\left(a\right)\cos\left(a\right)\sin\left(B\right)\cos\left(B\right)-\cos^2\left(a\right)\sin^2\left(B\right)=\sin^2\left(a\right)-\sin^2\left(B\right)\"> Foil\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin^2\left(a\right)\cos^2\left(B\right)-\cos^2\left(a\right)\sin^2\left(B\right)=\sin^2\left(a\right)-\sin^2\left(B\right)\"> Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin^2\left(a\right)\left(1-\sin^2\left(B\right)\right)-\left(1-\sin^2\left(a\right)\right)\sin^2\left(B\right)=\sin^2\left(a\right)-\sin^2\left(B\right)\">  Replace <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \cos^2\left(B\right)\"> with <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 1-\sin^2\left(B\right)\">. Replace <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \cos^2\left(a\right)\"> with <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 1-\sin^2\left(a\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE  \sin^2\left(a\right)-\sin^2\left(a\right)\sin^2\left(B\right)-\sin^2\left(B\right)+\sin^2\left(a\right)\sin^2\left(B\right)=\sin^2\left(a\right)-\sin^2\left(B\right)\"> Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE  \sin^2\left(a\right)-\sin^2\left(B\right)=\sin^2\left(a\right)-\sin^2\left(B\right)\"> Combine like terms\r<BR>\n" );
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document.write( "So we've just proven that \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sin\left(a+B\right)\sin\left(a-B\right)=\sin^2\left(a\right)-\sin^2\left(B\right)\"> \r<BR>\n" );
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document.write( "is an identity.\r<BR>\n" );
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