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Mathematics
Problem
Let
y
=
(
sin
x
1
+
cos
x
)
tan
x
y=\left(\dfrac{\sin x}{1+\cos x}\right)^{\tan x}
y
=
(
1
+
cos
x
sin
x
)
t
a
n
x
. Evaluate
y
′
y'
y
′
at
x
=
π
4
x=\dfrac{\pi}{4}
x
=
4
π
. a)
(
2
−
1
)
[
2
ln
(
2
−
1
)
+
2
2
]
(\sqrt2-1)[2\ln(\sqrt2-1)+2\sqrt2]
(
2
−
1
)
[
2
ln
(
2
−
1
)
+
2
2
]
b)
(
2
−
1
)
[
ln
(
2
−
1
)
+
2
]
(\sqrt2-1)[\ln(\sqrt2-1)+\sqrt2]
(
2
−
1
)
[
ln
(
2
−
1
)
+
2
]
c)
(
2
−
1
)
[
2
ln
(
2
−
1
)
+
2
]
(\sqrt2-1)[2\ln(\sqrt2-1)+\sqrt2]
(
2
−
1
)
[
2
ln
(
2
−
1
)
+
2
]
d)
(
2
−
1
)
[
2
ln
(
2
+
1
)
+
2
]
(\sqrt2-1)[2\ln(\sqrt2+1)+\sqrt2]
(
2
−
1
)
[
2
ln
(
2
+
1
)
+
2
]
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