- #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
Click For Summary
Trig identities can indeed be proven using basic trigonometric functions, as demonstrated by the transformation of the expression involving tangent and secant. The equation simplifies to show that the left-hand side equals negative cosine of double the angle. This highlights the interconnectedness of trigonometric functions in proving identities. The discussion emphasizes the efficiency of the proof process, suggesting that quicker methods may exist. Overall, the conversation reinforces the validity of using fundamental trigonometric functions for identity 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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