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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
sin
x
+
cos
x
−
2
sin
x
−
cos
x
f(x) = \frac{\sin x + \cos x - \sqrt{2}}{\sin x - \cos x}
f
(
x
)
=
s
i
n
x
−
c
o
s
x
s
i
n
x
+
c
o
s
x
−
2
,
x
∈
[
0
,
π
]
−
{
π
4
}
x \in [0, \pi] - \left\{\frac{\pi}{4}\right\}
x
∈
[
0
,
π
]
−
{
4
π
}
. Then
f
(
7
π
12
)
f
′
′
(
7
π
12
)
f\left(\frac{7\pi}{12}\right)f''\left(\frac{7\pi}{12}\right)
f
(
12
7
π
)
f
′′
(
12
7
π
)
is equal to : (1)
−
2
3
-\frac{2}{3}
−
3
2
(2)
2
9
\frac{2}{9}
9
2
(3)
−
1
3
3
-\frac{1}{3\sqrt{3}}
−
3
3
1
(4)
−
2
3
3
\frac{-2}{3\sqrt{3}}
3
3
−
2
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