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  2. Proofs of trigonometric identities - Wikipedia

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

    The sign of the square root needs to be chosen properly—note that if 2 π is added to θ, the quantities inside the square roots are unchanged, but the left-hand-sides of the equations change sign. Therefore, the correct sign to use depends on the value of θ.

  3. List of trigonometric identities - Wikipedia

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

    The half-angle formula for cosine can be obtained by replacing with / and taking the square-root of both sides: ⁡ (/) = (+ ⁡) /. Sine power-reduction formula: an illustrative diagram. The shaded blue and green triangles, and the red-outlined triangle E B D {\displaystyle EBD} are all right-angled and similar, and all contain the angle θ ...

  4. Law of tangents - Wikipedia

    en.wikipedia.org/wiki/Law_of_tangents

    In trigonometry, the law of tangents or tangent rule [1] is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides. In Figure 1, a, b, and c are the lengths of the three sides of the triangle, and α, β, and γ are the angles opposite those three respective sides.

  5. Pythagorean trigonometric identity - Wikipedia

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

    In this way, this trigonometric identity involving the tangent and the secant follows from the Pythagorean theorem. The angle opposite the leg of length 1 (this angle can be labeled φ = π/2 − θ) has cotangent equal to the length of the other leg, and cosecant equal to the length of the hypotenuse. In that way, this trigonometric identity ...

  6. Mollweide's formula - Wikipedia

    en.wikipedia.org/wiki/Mollweide's_formula

    In trigonometry, Mollweide's formula is a pair of relationships between sides and angles in a triangle. [1] [2]A variant in more geometrical style was first published by Isaac Newton in 1707 and then by Friedrich Wilhelm von Oppel [] in 1746.

  7. Idaho abortion trafficking law partly revived by US appeals court

    www.aol.com/news/idaho-abortion-trafficking-law...

    December 2, 2024 at 8:13 PM. By Brendan Pierson (Reuters) -Idaho can enforce a first-of-its-kind "abortion trafficking" law against those who harbor or transport a minor to get an abortion out of ...

  8. Pitot theorem - Wikipedia

    en.wikipedia.org/wiki/Pitot_theorem

    A tangential quadrilateral is usually defined as a convex quadrilateral for which all four sides are tangent to the same inscribed circle. Pitot's theorem states that, for these quadrilaterals, the two sums of lengths of opposite sides are the same. Both sums of lengths equal the semiperimeter of the quadrilateral. [2]

  9. Broadcom forecasts Q1 revenue above estimates on strong AI ...

    www.aol.com/news/broadcom-forecasts-first...

    By Arsheeya Bajwa and Zaheer Kachwala (Reuters) -Broadcom forecast quarterly revenue above Wall Street estimates on Thursday and predicted booming demand for its custom artificial intelligence ...