Dilucidationes super formulis, quibus sinus et cosinus angulorum multiplorum exprimi solent, ubi simul ingentes difficultates diluuntur
Elucidations about the formula, in which the sines and cosines of angles are to be multiplied, where at once large difficulties are diluted
Euler begins by deriving a polynomial expansion for 2 cos(nφ). He then substitutes z for cos(φ) and s = cos(nφ) and obtains a second order differential equation. He tries to solve that with unknown coefficients and gets another series for cos(nφ).
Original Source Citation
Nova Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 9, pp. 54-80.
Opera Omnia Citation
Series 1, Volume 16A, pp.282-310.