SOLUTION: I posted earlier: In proving a trig identity, why is working only one side important? Can you provide an example where working both sides gives a different result than workin

Question 889370: I posted earlier:
In proving a trig identity, why is working only one side important?
Can you provide an example where working both sides gives a different result than working on only one side?
I've searched online and have not found any reason to work on only one side of the equation.
I saw some comments that you "should" do that, but no reason for it.
I have done several identity proofs and I cannot see any difference. One of the basic tenets of algebra is that if you do the same operation to both sides, it's still equal.
I suspect it's just some superstition, like stepping on a crack.
If I lose points in class for doing both sides, I'll argue it there.
Found 2 solutions by josgarithmetic, Alan3354:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Way too many possible identities for any tutor to choose from. Give us one from your textbook. Maybe two from the book.

An identity to check or to prove will be an expression on the left, an expression on the right, and an EQUALITY symbol in the middle. Your goal is to show that these expressions are equal. You can start with the right side, or you can start with the left side. Maybe to start with the left side is simply a convention. Pick a side; either side; stay with it.

Transform one side using algebra and other identities until you are able to make the expression match the expression shown on the other side. Doing this successfully means that the two original expressions on both sides of the equality symbol are equal, and that the original equation is an identity.

You should avoid messing with both expressions because this just confuses your steps. Your goal, remember, is to show that the one side is the same meaning as the other side.

The goal for an equation is usually to find a formula for one of the variables or to solve for a variable (like get its value). The goal for proving an identity is to find if two expressions are equal - NOT to solve an equation. You will use algebra number properties and identities for both goals.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
gibberish from josg...
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Can anyone give an example where working only 1 side versus both makes a difference?
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I can't.

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