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Mathematics
Problem
A function
f
(
x
)
f(x)
f
(
x
)
satisfies
f
(
x
)
=
sin
x
+
∫
0
x
f
′
(
t
)
(
2
sin
t
−
sin
2
t
)
d
t
f(x) = \sin x + \int_{0}^{x} f'(t)(2\sin t - \sin^2 t) dt
f
(
x
)
=
sin
x
+
∫
0
x
f
′
(
t
)
(
2
sin
t
−
sin
2
t
)
d
t
, then
f
(
x
)
f(x)
f
(
x
)
is a.
x
1
−
sin
x
\frac{x}{1-\sin x}
1
−
s
i
n
x
x
b.
sin
x
1
−
sin
x
\frac{\sin x}{1-\sin x}
1
−
s
i
n
x
s
i
n
x
c.
1
−
cos
x
cos
x
\frac{1-\cos x}{\cos x}
c
o
s
x
1
−
c
o
s
x
d.
tan
x
1
−
sin
x
\frac{\tan x}{1-\sin x}
1
−
s
i
n
x
t
a
n
x
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