Tangent Half-angle Formula
In trigonometry, the tangent half-angle formulas relate the tangent of one half on an angle to trigonometric functions of the entire angle, as follows:
Read more about Tangent Half-angle Formula: Forms of The Identity, The Weierstrass Substitution, Hyperbolic Identities, The Gudermannian Function
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“Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective positions of the beings which compose it, if moreover this intelligence were vast enough to submit these data to analysis, it would embrace in the same formula both the movements of the largest bodies in the universe and those of the lightest atom; to it nothing would be uncertain, and the future as the past would be present to its eyes.”
—Pierre Simon De Laplace (1749–1827)