document.write( "Question 35523: Prove the following is an Identity:\r
\n" ); document.write( "\n" ); document.write( "Tan (X) - Cot (X) over Tan (X) + Cot (X) = 2sin^2 (X) - 1 \n" ); document.write( "
Algebra.Com's Answer #21686 by narayaba(40)\"\" \"About 
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Tan (X) - Cot (X) / Tan (X) + Cot (X)-------------------(1)\r
\n" ); document.write( "\n" ); document.write( "Cot (X) = 1/Tan (X)\r
\n" ); document.write( "\n" ); document.write( "pluggin in for Cot(X) in (1)\r
\n" ); document.write( "\n" ); document.write( "(Tan(X) - 1/Tan(X)) / (Tan(X) + 1/Tan(X))\r
\n" ); document.write( "\n" ); document.write( "=((Tan^2(X) - 1)/Tan(X)) / ((Tan^2(X) + 1)/Tan (X))\r
\n" ); document.write( "\n" ); document.write( "=(Tan^2(X) - 1)/ (Tan^2(X) + 1) \r
\n" ); document.write( "\n" ); document.write( "=(Tan^2(X) - 1)/ Sec^2(X)\r
\n" ); document.write( "\n" ); document.write( "=cos^2(X) * (Tan^2(X) - 1)\r
\n" ); document.write( "\n" ); document.write( "=cos^2(X) * ((sin^2(X)/cos^2(X)) - 1)\r
\n" ); document.write( "\n" ); document.write( "=sin^2(X) - cos^2(X) = sin^2(X) - (1- sin^2(X)) = 2sin^2(X) - 1\r
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