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Problem
Problem
If the functions
f
(
x
)
f(x)
f
(
x
)
and
g
(
x
)
g(x)
g
(
x
)
are defined on
R
→
R
R \rightarrow R
R
→
R
such that
f
(
x
)
=
cos
2
x
+
cos
2
(
x
+
2
π
3
)
+
cos
2
(
x
−
2
π
3
)
+
cos
2
5
π
4
f(x) = \cos^2 x + \cos^2\left(x + \frac{2\pi}{3}\right) + \cos^2\left(x - \frac{2\pi}{3}\right) + \cos^2 \frac{5\pi}{4}
f
(
x
)
=
cos
2
x
+
cos
2
(
x
+
3
2
π
)
+
cos
2
(
x
−
3
2
π
)
+
cos
2
4
5
π
and
g
(
2
)
=
−
1
g(2) = -1
g
(
2
)
=
−
1
, then the value of
cot
−
1
(
g
(
f
(
1
)
)
)
+
cos
−
1
(
g
(
f
(
2
)
)
)
\cot^{-1}(g(f(1))) + \cos^{-1}(g(f(2)))
cot
−
1
(
g
(
f
(
1
)))
+
cos
−
1
(
g
(
f
(
2
)))
is equal to (a)
3
π
4
\frac{3\pi}{4}
4
3
π
(b)
5
π
4
\frac{5\pi}{4}
4
5
π
(c)
3
π
2
\frac{3\pi}{2}
2
3
π
(d)
7
π
4
\frac{7\pi}{4}
4
7
π
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