document.write( "Question 889493: Prove the identity: \r
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document.write( "Tan^2(x)/(1+tan^2(x)) = sin^2(x) \n" );
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Algebra.Com's Answer #538200 by Theo(13342)![]() ![]() You can put this solution on YOUR website! \r \n" ); document.write( "\n" ); document.write( "you will use the identiTy tan^2(x) + 1 = sec^2(x)\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "your equation becomes:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "tan^2(x) / sec^(x) = sin^2(x)\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "since sec^(x) = 1/cos^2(x), your equation becomes:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "tan^2(x) * cos^2(x) = sin^2(x)\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "since tan^2(x) = sin^2(x) / cos^2(x), your equation becomes:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "sin^2(x) / cos^2(x) * cos^2(x) = sin^2(x)\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "the cos^2(x) in the numerator and denominator cancel out and you are left with:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "sin^2(x) = sin^2(x)\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "QED (means proof is done)\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |