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Figure 7b cuts a hexagon in two different ways into smaller pieces, yielding a proof of the law of cosines in the case that the angle γ is obtuse. We have in pink, the areas a 2, b 2, and −2ab cos γ on the left and c 2 on the right; in blue, the triangle ABC twice, on the left, as well as on the right.
2.5 Proof of compositions of trig and inverse trig functions. ... Printable version; ... Proof 2: Refer to the triangle diagram above.
Date/Time Thumbnail Dimensions User Comment; current: 02:01, 16 December 2007: 320 × 180 (1 KB): Ttbya {{Information |Description=Image describing the w:en:Law of cosines |Source=self-made |Date=December 16, 2007 |Permission=See below. |other_versions=Image:Triangle with trigonometric proof of the law of cosines.png}} Vectorized version of the
English: Image to demonstrate the law of cosines of plane trigonometry. Only one of the three equalities is shown; the other two are proved in the same way, taking the other two sides of the triangle as its base.
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.
The proof (Todhunter, [1] Art.49) of the first formula starts from the identity = , using the cosine rule to express A in terms of the sides and replacing the sum of two cosines by a product. (See sum-to-product identities .)
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.
The following outline is provided as an overview of and topical guide to trigonometry: . Trigonometry – branch of mathematics that studies the relationships between the sides and the angles in triangles.
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