document.write( "Question 1202859: Prove each identity:\r
\n" ); document.write( "\n" ); document.write( "tan^2(x)/1+tan^2(x) =sin^2(x)\r
\n" ); document.write( "\n" ); document.write( "and \r
\n" ); document.write( "\n" ); document.write( "sin^2(x)(1+1/tan^2(x))=1\r
\n" ); document.write( "\n" ); document.write( "i get confused for example sin^2(x) and (sinx)^2 \n" ); document.write( "
Algebra.Com's Answer #838038 by greenestamps(13216)\"\" \"About 
You can put this solution on YOUR website!


\n" ); document.write( "Preliminary comments....

\n" ); document.write( "(1) \"sin^2(x)\" and (sinx)^2 are both used to represent the square of sin(x).

\n" ); document.write( "(2) Use parentheses properly. The first equation as you show it is not an identity:

\n" ); document.write( "tan^2(x)/1+tan^2(x) =sin^2(x) ---> \"tan%5E2%28x%29%2F1%2Btan%5E2%28x%29=sin%5E2%28x%29\"

\n" ); document.write( "The equation you intended to show is

\n" ); document.write( "tan^2(x)/(1+tan^2(x)) =sin^2(x) ---> \"tan%5E2%28x%29%2F%281%2Btan%5E2%28x%29%29=sin%5E2%28x%29\"

\n" ); document.write( "Now my approaches to these....

\n" ); document.write( "Both of the other tutors used the identity 1+tan^2(x) = sec^2(x). That is certainly one way to start. But after that they turn everything into sines and cosines, so it seems easiest just to do that at the beginning.

\n" ); document.write( "(a) \"tan%5E2%28x%29%2F%281%2Btan%5E2%28x%29%29\"

\n" ); document.write( "\"%28sin%5E2%28x%29%2Fcos%5E2%28x%29%29%2F%281%2Bsin%5E2%28x%29%2Fcos%5E2%28x%29%29\"

\n" ); document.write( "

\n" ); document.write( "\"%28sin%5E2%28x%29%2Fcos%5E2%28x%29%29%2F%281%2Fcos%5E2%28x%29%29\"

\n" ); document.write( "\"sin%5E2%28x%29\"

\n" ); document.write( "(b) \"sin%5E2%28x%29%281%2B1%2Ftan%5E2%28x%29%29\"

\n" ); document.write( "\"sin%5E2%28x%29%281%2B%28cos%5E2%28x%29%2Fsin%5E2%28x%29%29%29\"

\n" ); document.write( "\"sin%5E2%28x%29%2Bcos%5E2%28x%29=1\"

\n" ); document.write( " \n" ); document.write( "
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