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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
cos
(
tan
−
1
(
sin
(
cot
−
1
x
)
)
)
f(x) = \cos(\tan^{-1}(\sin(\cot^{-1}x)))
f
(
x
)
=
cos
(
tan
−
1
(
sin
(
cot
−
1
x
)))
. The simplest form of
f
(
x
)
f(x)
f
(
x
)
can be written as
(
x
2
+
A
x
2
+
B
)
1
/
2
\left(\frac{x^2 + A}{x^2 + B}\right)^{1/2}
(
x
2
+
B
x
2
+
A
)
1/2
. The value of
(
A
+
B
)
(A + B)
(
A
+
B
)
is _______. (1) 1 (2) 2 (3) 3 (4) 0
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