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Motivation behind the question: I've wondered since grade 10 that if $\sin(a+b),\sin(a-b)$ have formulas in terms of $\sin(a)$ and $\sin(b)$, then why not $\sin(ab)$. But I couldn't find any such information sadly.
My attempt:-
$$\sin(ab)=\sin\bigg(\frac{(a+b)^2}{4}-\frac{(a-b)^2}{4}\bigg)$$
This...
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Motivation behind the question: I've wondered since grade 10 that if $\sin(a+b),\sin(a-b)$ have formulas in terms of $\sin(a)$ and $\sin(b)$, then why not $\sin(ab)$. But I couldn't find any such information sadly.
My attempt:-
$$\sin(ab)=\sin\bigg(\frac{(a+b)^2}{4}-\frac{(a-b)^2}{4}\bigg)$$
This...
What I am looking for is, for example, $\sin(xy)=f(x)g(y)$, where $f$ and $y$ are some functions for $x$ and $y$.
It is "trivial" to see the answer is no, but not really able to come up with a reasonable reason.
In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths.
More formally, let
U
{\displaystyle U}
and
V
{\displaystyle V}
be open subsets of
R
n
{\displaystyle \mathbb {R} ^{n}}
. A function
f
:
U
→
V
{\displaystyle f:U\to V}
is called conformal (or angle-preserving) at...
In mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space.
In a real two dimensional space, conformal geometry is precisely the geometry of Riemann surfaces. In space higher than two dimensions, conformal geometry may refer either to the study of conformal transformations of what are called "flat spaces" (such as Euclidean spaces or spheres), or to the study of conformal manifolds which are Riemannian or pseudo-Riemannian manifolds with a class of metrics that are defined up to scale. Study of the flat structures is sometimes termed Möbius...
0
