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Mathematics
Mathematics
Problem
Consider
f
(
x
)
=
tan
−
1
(
1
+
sin
x
1
−
sin
x
)
f(x) = \tan^{-1}\left(\sqrt{\frac{1+\sin x}{1-\sin x}}\right)
f
(
x
)
=
tan
−
1
(
1
−
s
i
n
x
1
+
s
i
n
x
)
,
x
∈
(
0
,
π
2
)
x \in \left(0, \frac{\pi}{2}\right)
x
∈
(
0
,
2
π
)
. A normal to
y
=
f
(
x
)
y = f(x)
y
=
f
(
x
)
at
x
=
π
6
x = \frac{\pi}{6}
x
=
6
π
also passes through the point: (a)
(
π
6
,
0
)
\left(\frac{\pi}{6}, 0\right)
(
6
π
,
0
)
(b)
(
π
4
,
0
)
\left(\frac{\pi}{4}, 0\right)
(
4
π
,
0
)
(c)
(
0
,
0
)
(0, 0)
(
0
,
0
)
(d)
(
0
,
2
π
3
)
\left(0, \frac{2\pi}{3}\right)
(
0
,
3
2
π
)
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