"The sum and difference formulas are vital to building trigonometric tables finer than the traditional 24 entries per 90°. ...they can also be used to generate many other identities. In particular, formulas for Sin 2θ, Cos 2θ, Sin 3θ, Cos 3θ, and higher multiples may be generated simply by writing nθ = θ + θ +... + θ and applying the sum formulas repeatedly. This was done by... KamalÄkara in his SiddhÄnta-Tattva-Viveka (1658) up to the sine and cosine of 5θ; he quotes (who clearly knew this could be done) for the addition and subtraction laws. KamalÄkara's sine triple-angle formula...wasSin\,3\theta = Sin\,\theta(3 - \frac{(Sin\,\theta)^2}{(Sin\,30^o)^2}),equivalent to the modern formulasin\,3\theta = 3sin\,\theta - 4sin^3\,\theta; ...The identity ...has special significance, since it may be used to get an accurate estimate of sin 1° from sin 3°āprovided one is able to solve cubic equations."
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Glen Van Brummelen, The Mathematics of the Heavens and the Earth: The Early History of Trigonometry (2009) Ch. 3 India, p.107. Also see angle trisection.
https://en.wikiquote.org/wiki/History_of_mathematics
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History of mathematics
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