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Mathematics
Mathematics
Problem
If
f
(
x
)
=
−
∫
0
x
log
(
cos
t
)
d
t
f(x) = -\int_0^x \log (\cos t) \, dt
f
(
x
)
=
−
∫
0
x
lo
g
(
cos
t
)
d
t
, then the value of
f
(
x
)
−
2
f
(
π
4
+
x
2
)
+
2
f
(
π
4
−
x
2
)
f(x) - 2f\left(\frac{\pi}{4} + \frac{x}{2}\right) + 2f\left(\frac{\pi}{4} - \frac{x}{2}\right)
f
(
x
)
−
2
f
(
4
π
+
2
x
)
+
2
f
(
4
π
−
2
x
)
is equal to a.
−
x
log
2
-x \log 2
−
x
lo
g
2
b.
x
2
log
2
\frac{x}{2} \log 2
2
x
lo
g
2
c.
x
3
log
2
\frac{x}{3} \log 2
3
x
lo
g
2
d. None of these
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