MathDB
Problems
Contests
International Contests
Pan African
2000 Pan African
1
1
Part of
2000 Pan African
Problems
(2)
Trig Equation
Source: Pan African 2000
10/3/2005
Solve for
x
∈
R
x \in R
x
∈
R
:
sin
3
x
(
1
+
cot
x
)
+
cos
3
x
(
1
+
tan
x
)
=
cos
2
x
\sin^3{x}(1+\cot{x})+\cos^3{x}(1+\tan{x})=\cos{2x}
sin
3
x
(
1
+
cot
x
)
+
cos
3
x
(
1
+
tan
x
)
=
cos
2
x
trigonometry
System of equations
Source: Pan African 2000
10/3/2005
Let
a
a
a
,
b
b
b
and
c
c
c
be real numbers such that
a
2
+
b
2
=
c
2
a^2+b^2=c^2
a
2
+
b
2
=
c
2
, solve the system:
z
2
=
x
2
+
y
2
z^2=x^2+y^2
z
2
=
x
2
+
y
2
(
z
+
c
)
2
=
(
x
+
a
)
2
+
(
y
+
b
)
2
(z+c)^2=(x+a)^2+(y+b)^2
(
z
+
c
)
2
=
(
x
+
a
)
2
+
(
y
+
b
)
2
in real numbers
x
,
y
x, y
x
,
y
and
z
z
z
.
inequalities