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Vietnam National Olympiad
1975 Vietnam National Olympiad
5
5
Part of
1975 Vietnam National Olympiad
Problems
(1)
min and max of tan(3x)/tan^3x in (0, \pi /2)
Source: Vietnamese MO (VMO) 1975 P5
8/20/2018
Show that the sum of the (local) maximum and minimum values of the function
t
a
n
(
3
x
)
t
a
n
3
x
\frac{tan(3x)}{tan^3x}
t
a
n
3
x
t
an
(
3
x
)
on the interval
(
0
,
π
2
)
\big(0, \frac{\pi }{2}\big)
(
0
,
2
π
)
is rational.
algebra
function
minimum value
maximum value
analysis