Tag: Series: Sine Angle Product Formula

Math

Sine Angle Product Formula 3

Post author By Nihal Uppugunduri
Post date September 4, 2025
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In this post, we continue the discussion from a previous post about the existence of a suitable sine angle product identity.

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Math

Sine Angle Product Formula 2

Post author By Nihal Uppugunduri
Post date March 14, 2023
No Comments on Sine Angle Product Formula 2

In this post, we continue the discussion from a previous post about the existence of a suitable sine angle product identity.

Tags Hidden From Main Subject Pages, Series: Sine Angle Product Formula, Studies

Math

Sine Angle Product Formula

Post author By Nihal Uppugunduri
Post date December 1, 2022
No Comments on Sine Angle Product Formula

In this post, we address the following question: does there exist a polynomial identity for $\sin(ab)$ in terms of $\sin a,\cos a,\sin b,\cos b$ like for the single angle addition formula? Formulated rigorously, does there exist a polynomial $P$ such that $\sin(ab) = P\left( \sin a,\cos a,\sin b,\cos b \right)$ for all $a,b$ ? We suspect that $P$ does not exist, which we try to show here. (Actually, a more general question that is worth discussing is whether there exists a rational identity for $\sin(ab)$ , e.g. with $P$ replaced by a rational function. But we discuss polynomial for now.)

Tags Series: Sine Angle Product Formula, Studies