MathDB
Problems
Contests
National and Regional Contests
Belgium Contests
Flanders Math Olympiad
2020 Flanders Math Olympiad
1
1
Part of
2020 Flanders Math Olympiad
Problems
(1)
1/9 sin^4 x + 1/16 cos^4 x = 1/25
Source: Flanders Math Olympiad 2020 p1
12/24/2022
Let
x
x
x
be an angle between
0
o
0^o
0
o
and
9
0
o
90^o
9
0
o
so that
sin
4
x
9
+
cos
4
x
16
=
1
25
.
\frac{\sin^4 x}{9}+\frac{\cos^4 x}{16 }=\frac{1}{25} .
9
sin
4
x
+
16
cos
4
x
=
25
1
.
Then what is
tan
x
\tan x
tan
x
?
trigonometry