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Statements
1
2
α
2
arcsin
(
ζ
α
)
+
1
2
ζ
(
α
2
-
ζ
2
)
1
/
2
=
arcsin
(
x
a
)
-
(
1
-
a
2
)
1
/
2
arctan
(
x
(
1
-
a
2
a
2
-
x
2
)
1
/
2
)
,
1
2
superscript
𝛼
2
𝜁
𝛼
1
2
𝜁
superscript
superscript
𝛼
2
superscript
𝜁
2
1
2
𝑥
𝑎
superscript
1
superscript
𝑎
2
1
2
𝑥
superscript
1
superscript
𝑎
2
superscript
𝑎
2
superscript
𝑥
2
1
2
{\displaystyle{\displaystyle\frac{1}{2}\alpha^{2}\operatorname{arcsin}\left(%
\frac{\zeta}{\alpha}\right)+\frac{1}{2}\zeta\left(\alpha^{2}-\zeta^{2}\right)^%
{1/2}=\operatorname{arcsin}\left(\frac{x}{a}\right)-\left(1-a^{2}\right)^{1/2}%
\operatorname{arctan}\left(x\left(\frac{1-a^{2}}{a^{2}-x^{2}}\right)^{1/2}%
\right),}}
-
α
≤
ζ
≤
α
𝛼
𝜁
𝛼
{\displaystyle{\displaystyle-\alpha\leq\zeta\leq\alpha}}
arcsin
z
𝑧
{\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}
arctan
z
𝑧
{\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
x
𝑥
{\displaystyle{\displaystyle x}}
a
𝑎
{\displaystyle{\displaystyle a}}
ζ
𝜁
{\displaystyle{\displaystyle\zeta}}
α
𝛼
{\displaystyle{\displaystyle\alpha}}
Identifiers
