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Problem
Problem
Prove that
tan
−
1
y
z
x
r
+
tan
−
1
z
x
y
r
+
tan
−
1
x
y
z
r
=
π
2
,
where
x
2
+
y
2
+
z
2
=
r
2
.
\tan^{-1}\frac{yz}{xr}+\tan^{-1}\frac{zx}{yr}+\tan^{-1}\frac{xy}{zr}=\frac{\pi}{2},\ \text{where } x^2+y^2+z^2=r^2.
tan
−
1
x
r
y
z
+
tan
−
1
y
r
z
x
+
tan
−
1
z
r
x
y
=
2
π
,
where
x
2
+
y
2
+
z
2
=
r
2
.
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