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2020 Moldova Team Selection Test
5
5
Part of
2020 Moldova Team Selection Test
Problems
(1)
Trigonometry with natural parameter
Source: Moldova TST 2020
3/7/2020
Let
n
n
n
be a natural number. Find all solutions
x
x
x
of the system of equations
{
s
i
n
x
+
c
o
s
x
=
n
2
t
g
x
2
=
n
−
2
3
\left\{\begin{matrix} sinx+cosx=\frac{\sqrt{n}}{2}\\tg\frac{x}{2}=\frac{\sqrt{n}-2}{3}\end{matrix}\right.
{
s
in
x
+
cos
x
=
2
n
t
g
2
x
=
3
n
−
2
On interval
[
0
,
π
4
)
.
\left[0,\frac{\pi}{4}\right).
[
0
,
4
π
)
.
trigonometry
algebra
system of equations
parameterization