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National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
1994 Swedish Mathematical Competition
3
3
Part of
1994 Swedish Mathematical Competition
Problems
(1)
sin^2c = sin^2a + sin^2b
Source: 1994 Swedish Mathematical Competition p3
4/2/2021
The vertex
B
B
B
of the triangle
A
B
C
ABC
A
BC
lies in the plane
P
P
P
. The plane of the triangle meets the plane in a line
L
L
L
. The angle between
L
L
L
and
A
B
AB
A
B
is a, and the angle between
L
L
L
and
B
C
BC
BC
is
b
b
b
. The angle between the two planes is
c
c
c
. Angle
A
B
C
ABC
A
BC
is
9
0
o
90^o
9
0
o
. Show that
sin
2
c
=
sin
2
a
+
sin
2
b
\sin^2c = \sin^2a + \sin^2b
sin
2
c
=
sin
2
a
+
sin
2
b
. https://cdn.artofproblemsolving.com/attachments/9/e/c0608e5408fd27a5f907a3488cce7dc2af6953.png
trigonometry
geometry