- #31
Evangeline101
- 112
- 5
Student100 said:
what do you mean?
How Do You Prove Trigonometric Identities with Minimal Equations?
- Thread starter alexandria
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SUMMARY
The forum discussion centers on proving the trigonometric identity tan(x) - 1. Participants emphasize the importance of manipulating the right side of the equation while keeping the left side intact. Key techniques include using the difference of squares formula and factoring expressions. The final correct form of the identity is established as (tan(x) - 1)(tan(x) + 1) / (tan(x) + 1) = tan(x) - 1, confirming the identity.
PREREQUISITES- Understanding of trigonometric identities, specifically sin^2(x) + cos^2(x) = 1
- Familiarity with algebraic manipulation, including factoring and simplifying expressions
- Knowledge of the difference of squares formula: a^2 - b^2 = (a - b)(a + b)
- Ability to work with rational expressions and cross-multiplication
- Study the difference of squares in-depth to enhance algebraic manipulation skills
- Learn about other trigonometric identities and their proofs, such as the Pythagorean identities
- Practice solving trigonometric equations using various algebraic techniques
- Explore advanced topics in trigonometry, such as inverse trigonometric functions and their properties
Students studying trigonometry, educators teaching trigonometric identities, and anyone looking to improve their algebraic manipulation skills in mathematics.
what do you mean?
- #32
Student100
Education Advisor
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Evangeline101 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. No sense losing points on a typo. =)
The fixed solution looks fine to me.
- #33
Evangeline101
- 112
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Student100 said:
Okay, thanks for the help! :)
- #34
Evangeline101
- 112
- 5
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
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
Last edited:
- #35
epenguin
Science Advisor
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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.
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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