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  2. Pythagorean trigonometric identity - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_trigonometric...

    Similar right triangles illustrating the tangent and secant trigonometric functions Trigonometric functions and their reciprocals on the unit circle. The Pythagorean theorem applied to the blue triangle shows the identity 1 + cot 2 θ = csc 2 θ, and applied to the red triangle shows that 1 + tan 2 θ = sec 2 θ.

  3. Proofs of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/Proofs_of_trigonometric...

    There are several equivalent ways for defining trigonometric functions, and the proofs of the trigonometric identities between them depend on the chosen definition. The oldest and most elementary definitions are based on the geometry of right triangles and the ratio between their sides.

  4. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    Proof of the sum-and-difference-to-product cosine identity for prosthaphaeresis calculations using an isosceles triangle. The product-to-sum identities [28] or prosthaphaeresis formulae can be proven by expanding their right-hand sides using the angle addition theorems.

  5. Students discover and publish unexpected proof for 2,000-year ...

    www.aol.com/students-discover-publish-unexpected...

    Ne’Kiya Jackson and Calcea Johnson have published a paper on a new way to prove the 2000-year-old Pythagorean theorem. Their work began in a high school math contest.

  6. Identity (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Identity_(mathematics)

    Visual proof of the Pythagorean identity: for any angle , the point (,) = (⁡, ⁡) lies on the unit circle, which satisfies the equation + =.Thus, ⁡ + ⁡ =. In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value for all values of the variables ...

  7. Theorem - Wikipedia

    en.wikipedia.org/wiki/Theorem

    The Pythagorean theorem has at least 370 known proofs. [1]In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. [a] [2] [3] The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems.

  8. 2025 NFL mock draft: Expert projections for Cam Ward ... - AOL

    www.aol.com/2025-nfl-mock-draft-expert-192129777...

    The 2025 NFL draft order was shaken up by a Raiders win over the Jaguars in Week 16. Here's how that's impacting NFL mock drafts.

  9. Which foods are considered 'healthy?' FDA issues new label ...

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    The Food and Drug Administration's new rules on "healthy" food labels are voluntary and are scheduled to take effect at the end of February.

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