B Are there multiple ways to verify a trig identity?

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Multiple methods exist to verify trigonometric identities, and while some approaches may be preferred by specific instructors, all correct methods are valid. The discussion highlights that verification should ideally start from one side of the equation to prove it equals the other side, avoiding tautological conclusions. Participants emphasize the importance of clear, reversible steps in proofs, suggesting that using symbols like "Leftrightarrow" can clarify the logical flow. The conversation also touches on the simplicity of certain identities, indicating that the verification process can vary in complexity. Ultimately, the focus remains on demonstrating equivalence through valid mathematical reasoning.
  • #31
ProfuselyQuarky said:
That makes plenty of sense :smile:

When I think about, it's not that difficult to determine whether a move is legit or not.
No, it's not. If the operation you apply to both sides of an equation is one-to-one, it's reversible. For example, adding a number to or subtracting a number from each side, multiplying each side by a nonzero number, and exponentiating each side are reversible operations. In contrast, squaring both sides of an equation is not reversible.
 
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  • #32
ProfuselyQuarky said:
When I think about, it's not that difficult to determine whether a move is legit or not.

If you do these by operating on only one side - the way trig has traditionally been taught - it's automatic.
 

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