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  2. Green's identities - Wikipedia

    en.wikipedia.org/wiki/Green's_identities

    Explicitly incorporating this definition in the Green's second identity with ε = 1 results in = (). In particular, this demonstrates that the Laplacian is a self-adjoint operator in the L 2 inner product for functions vanishing on the boundary so that the right hand side of the above identity is zero.

  3. Proofs of trigonometric identities - Wikipedia

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

    Then multiplying the numerator and denominator inside the square root by (1 + cos θ) and using Pythagorean identities leads to: ⁡ = ⁡ + ⁡. Also, if the numerator and denominator are both multiplied by (1 - cos θ), the result is:

  4. Pythagorean trigonometric identity - Wikipedia

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

    A calculation confirms that z(0) = 1, and z is a constant so z = 1 for all x, so the Pythagorean identity is established. A similar proof can be completed using power series as above to establish that the sine has as its derivative the cosine, and the cosine has as its derivative the negative sine.

  5. 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.

  6. 7 Tips for Having More Energy - AOL

    www.aol.com/lifestyle/7-tips-having-more-energy...

    How to Have More Energy: 7 Tips. This article was reviewed by Craig Primack, MD, FACP, FAAP, FOMA. Life can get incredibly busy, and keeping up often hinges on having enough energy.

  7. 'Extraordinarily alarming': Mayorkas condemns social media ...

    www.aol.com/extraordinarily-alarming-mayorkas...

    Homeland Security Secretary Alejandro Mayorkas called language used by some social media users after Brian Thompson's death "extraordinarily alarming."

  8. Divergence theorem - Wikipedia

    en.wikipedia.org/wiki/Divergence_theorem

    A special case of this is =, in which case the theorem is the basis for Green's identities. With F → F × G {\displaystyle \mathbf {F} \rightarrow \mathbf {F} \times \mathbf {G} } for two vector fields F and G , where × {\displaystyle \times } denotes a cross product,

  9. 8 jewelry trends that are in for 2025 and 3 that are out ...

    www.aol.com/8-jewelry-trends-2025-3-140301428.html

    Personal and celebrity stylist Kim Appelt predicts a general trend toward convenience, comfort, and ease in 2025.. In other words, jewelry that goes with everything — like stacked gold pieces ...