document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117947>Question 117947</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sin^2x - sin^4x = (cos^2)(sin^2x)\r<BR>\n" );
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document.write( "sin^2x - (sin^2x)(sin^2x) = (cos^2x)(sin^2x)<BR>\n" );
document.write( "sin^2x - (sin^2x)(1/csc^2x) = (cos^2x)(1/csc^2x)<BR>\n" );
document.write( "sin^2x - (sin^2x/csc^2x) = (cos^2x / csc^2x)\r<BR>\n" );
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document.write( "cos^2x [sin^2x - (sin^2x / csc^2x) = (cos^2x / csc^2x)]\r<BR>\n" );
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document.write( "(sin^2x)(csc^2x) - sin^2x = cos^2x\r<BR>\n" );
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document.write( "(sin^2x)(csc^2x) = cos^2x + sin^2x\r<BR>\n" );
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document.write( "(sin^2x)(csc^2x) = 1\r<BR>\n" );
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document.write( "(1/csc^2x)(csc^2x/1) = 1\r<BR>\n" );
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document.write( "1 = 1\r<BR>\n" );
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document.write( "Can I prove the above identity this way? Or have I taken a leap of faith somewhere along the line?<BR>\n" );
document.write( "Thank you very much. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85972 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=85972\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When you prove identities, you only manipulate <b>one side</b>. So I'm going to change the left side into the right side\r<BR>\n" );
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document.write( "sin^2x - sin^4x = (cos^2x)(sin^2x).....Start with the given equation\r<BR>\n" );
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document.write( "sin^2x - (sin^2x)(sin^2x)  = (cos^2x)(sin^2x).....Rewrite sin^4x as (sin^2x)(sin^2x)\r<BR>\n" );
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document.write( "sin^2x(1 - sin^2x)  = (cos^2x)(sin^2x).....Factor out sin^2x\r<BR>\n" );
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document.write( "sin^2x(cos^2x)  = (cos^2x)(sin^2x).....Replace 1-sin^2x with cos^2x\r<BR>\n" );
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document.write( "(cos^2x)(sin^2x)  = (cos^2x)(sin^2x).....Rearrange the left side\r<BR>\n" );
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document.write( "So this verifies the identity\r<BR>\n" );
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document.write( " </SPAN>\n" );
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