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Mathematics
Mathematics
Problem
The function
f
(
x
)
=
ln
(
1
+
sin
2
x
)
−
ln
(
cos
2
x
)
f(x) = \ln(1 + \sin 2x) - \ln(\cos 2x)
f
(
x
)
=
ln
(
1
+
sin
2
x
)
−
ln
(
cos
2
x
)
,
∀
x
∈
(
0
,
π
4
)
\forall x \in \left(0, \frac{\pi}{4}\right)
∀
x
∈
(
0
,
4
π
)
, is the antiderivative of (a)
1
2
sec
2
x
\frac{1}{2}\sec 2x
2
1
sec
2
x
(b)
cosec
2
x
\operatorname{cosec} 2x
cosec
2
x
(c)
2
sec
2
x
2\sec 2x
2
sec
2
x
(d)
2
cosec
2
x
2\operatorname{cosec} 2x
2
cosec
2
x
(a)
1
2
sec
2
x
\frac{1}{2}\sec 2x
2
1
sec
2
x
(b)
cosec
2
x
\operatorname{cosec} 2x
cosec
2
x
(c)
2
sec
2
x
2\sec 2x
2
sec
2
x
(d)
2
cosec
2
x
2\operatorname{cosec} 2x
2
cosec
2
x
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