How Do You Prove Trigonometric Identities with Minimal Equations?

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The discussion focuses on proving a trigonometric identity, with participants sharing their attempts and seeking guidance. A key point is the suggestion to keep one side of the equation constant while manipulating the other side to achieve equality. Participants emphasize the importance of correctly applying trigonometric identities and factoring techniques, particularly the difference of squares. Confusion arises over specific steps, but clarification leads to the correct conclusion that the identity simplifies to tan(x) - 1. The thread highlights the collaborative effort in solving trigonometric problems and the value of clear communication in mathematical discussions.
  • #31
Student100 said:
That's fine. You just need to be careful, the = is saying something very precise.

what do you mean?
 
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  • #32
Evangeline101 said:
what do you mean?

The above line that I posted, you're saying the original expression is equal to 2tan(x), which isn't true. I know it was a typo, just make sure you're careful is all. No sense losing points on a typo. =)

The fixed solution looks fine to me.
 
  • #33
Student100 said:
The above line that I posted, you're saying the original expression is equal to 2tan(x), which isn't true. I know it was a typo, just make sure you're careful is all.

Okay, thanks for the help! :)
 
  • #34
Sorry for responding to this thread after it has been marked solved.

Ok, I am proving the exact same identity, I looked through the thread and the explanations were very helpful.

I wrote out the answer, and would just like to know if I have written the answer properly:

LS= tan x - 1
upload_2016-8-16_23-29-36.png
 
Last edited:
  • #35
Yes I think that's right now.
Hope you see it as simple now, and what you were missing.

One of the handful of formulae constantly useful to remember fluently, difference of two squares - and then difference of two n-th powers.
 

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