document.write( "Question 1131350: I'm working on trig identities. some are simple, some not.
\n" ); document.write( "I see comments about working on one side only. why is that?
\n" ); document.write( "Does it make a difference?
\n" ); document.write( "if so, can you show a problem wehre is does make a difference? \n" ); document.write( "

Algebra.Com's Answer #748018 by ikleyn(52800) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " It is interesting question.\r
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document.write( "Let assume that you are given a task to prove that two expressions are identical:\r\n" );
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document.write( "    A = B.\r\n" );
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document.write( "Expressions can be trigonometric or algebraic - it does not matter.\r\n" );
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document.write( "You can make transformations over the left side and over the right side.\r\n" );
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document.write( "If your transformations of each side are equivalent, and if they result to an identity\r\n" );
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document.write( "    C = D,\r\n" );
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document.write( "then you may conclude that the original expressions A and B are identical.\r\n" );
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document.write( "    Simply because you can reverse your chain of logical conclusions (= transformations) from\r\n" );
document.write( "     the identity  C = D  back to  A = B.\r\n" );
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document.write( "But if your transformations are  NOT equivalent and if they result to an identity\r\n" );
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document.write( "    C = D,\r\n" );
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document.write( "then you CAN NOT conclude that the original expressions are identical.\r\n" );
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\n" ); document.write( "\n" ); document.write( "So, working with equivalent transformations, you can transform either side or even both sides - there is NO obstacles
\n" ); document.write( "for it and for validity of your final conclusion.\r
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\n" ); document.write( "\n" ); document.write( "But if you work and use non-equivalent transformations on the way - then be careful - your final conclusion might be wrong.
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\n" ); document.write( "\n" ); document.write( "Regarding the example given by Edwin, he started from the hypothetical identity, squared both sides, obtained the identity -\r
\n" ); document.write( "\n" ); document.write( "but in this case he can not conclude that the original hypothetical identity is a real identity.\r
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\n" ); document.write( "\n" ); document.write( "Because squaring IS NOT an equivalent transformation: from $\"a%5E2\"$ = $\"b%5E2\"$ you can not conclude that a = b.\r
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