- #1
ttpp1124
- 110
- 4
- Homework Statement
- I believed I've proved it right, but can someone confirm?
- Relevant Equations
- n/a
Can Trig Identities Be Proven Using Basic Trigonometric Functions?
- Thread starter ttpp1124
- Start date
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SUMMARY
The discussion confirms that trigonometric identities can indeed be proven using basic trigonometric functions. Specifically, the identity \((\tan^2 x -1)/\sec^2 x = -\cos(2x)\) is established through a series of transformations involving \(\tan^2 x\), \(\sec^2 x\), and the Pythagorean identity. The proof demonstrates the efficiency of using fundamental trigonometric relationships to derive complex identities.
PREREQUISITES- Understanding of basic trigonometric functions: sine, cosine, tangent
- Familiarity with trigonometric identities and their applications
- Knowledge of the Pythagorean identity: \(\sin^2 x + \cos^2 x = 1\)
- Ability to manipulate algebraic expressions involving trigonometric functions
- Study the derivation of the double angle formulas for sine and cosine
- Explore advanced trigonometric identities and their proofs
- Learn about the unit circle and its relationship to trigonometric functions
- Practice solving trigonometric equations using identities
Students of mathematics, educators teaching trigonometry, and anyone interested in deepening their understanding of trigonometric identities and their proofs.
- #2
member 587159
I believe it is correct, but note that
$$(\tan^2 x -1)/\sec^2 x = (\tan^2 x -1) \cos^2 x = \sin^2 x - \cos^2 x = - \cos(2x)$$
so you could have been a little faster.
$$(\tan^2 x -1)/\sec^2 x = (\tan^2 x -1) \cos^2 x = \sin^2 x - \cos^2 x = - \cos(2x)$$
so you could have been a little faster.
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