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## Miscellaneous Exercise on Chapter 2 Prove that 9.
cot
−
1
(
1
+
sin
x
+
1
−
sin
x
1
+
sin
x
−
1
−
sin
x
)
=
x
2
,
x
∈
(
0
,
π
4
)
\cot ^{-1}\left(\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right)=\frac{x}{2}, x \in\left(0, \frac{\pi}{4}\right)
cot
−
1
(
1
+
s
i
n
x
−
1
−
s
i
n
x
1
+
s
i
n
x
+
1
−
s
i
n
x
)
=
2
x
,
x
∈
(
0
,
4
π
)
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