document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199745>Question 1199745</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove the identity: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28tan%28x%29%2B1%29%5E2=sec%5E2%28x%29%28cos%28x%29%2Bsin%28x%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28tan%28x%29%2B1%29%5E2=sec%5E2%28x%29%28cos%28x%29%2Bsin%28x%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833702 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=833702\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
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document.write( "The identity is fully confirmed.\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "To prove an identity, we alter one side only. The other side stays the same.<BR>\n" );
document.write( "The steps above show the left hand side (LHS) transforming into the right hand side (RHS).<BR>\n" );
document.write( "The RHS stays the same the entire time.\r<BR>\n" );
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document.write( "Since the RHS has cosine and sine, this is a hint to turn the tangent on the LHS into its equivalent form involving sine over cosine.<BR>\n" );
document.write( "tan = sin/cos<BR>\n" );
document.write( "which is of course the informal way to write this rule.\r<BR>\n" );
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document.write( "List of Trig Identities<BR>\n" );
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document.write( "Then I got each denominator the same at cos^2(x), and combined the fractions.\r<BR>\n" );
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document.write( "On the 6th step, I used the rule (a+b)^2 = a^2+2ab+b^2\r<BR>\n" );
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document.write( "On the last step, I used another trig identity of <BR>\n" );
document.write( "sec = 1/cos<BR>\n" );
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