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Statements
(
y
-
α
2
)
1
/
2
-
α
arctan
(
(
y
-
α
2
)
1
/
2
α
)
=
arccos
(
x
(
1
-
α
2
)
1
/
2
)
-
α
2
arccos
(
(
1
+
α
2
)
x
2
-
1
+
α
2
(
1
-
α
2
)
(
1
-
x
2
)
)
,
superscript
𝑦
superscript
𝛼
2
1
2
𝛼
superscript
𝑦
superscript
𝛼
2
1
2
𝛼
𝑥
superscript
1
superscript
𝛼
2
1
2
𝛼
2
1
superscript
𝛼
2
superscript
𝑥
2
1
superscript
𝛼
2
1
superscript
𝛼
2
1
superscript
𝑥
2
{\displaystyle{\displaystyle\left(y-\alpha^{2}\right)^{1/2}-\alpha%
\operatorname{arctan}\left(\frac{\left(y-\alpha^{2}\right)^{1/2}}{\alpha}%
\right)=\operatorname{arccos}\left(\frac{x}{\left(1-\alpha^{2}\right)^{1/2}}%
\right)-\frac{\alpha}{2}\operatorname{arccos}\left(\frac{\left(1+\alpha^{2}%
\right)x^{2}-1+\alpha^{2}}{\left(1-\alpha^{2}\right)\left(1-x^{2}\right)}%
\right),}}
y
≥
α
2
𝑦
superscript
𝛼
2
{\displaystyle{\displaystyle y\geq\alpha^{2}}}
arccos
z
𝑧
{\displaystyle{\displaystyle\operatorname{arccos}\NVar{z}}}
arctan
z
𝑧
{\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
x
𝑥
{\displaystyle{\displaystyle x}}
y
𝑦
{\displaystyle{\displaystyle y}}
α
𝛼
{\displaystyle{\displaystyle\alpha}}
