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Problem
Problem
Points
D
,
E
D, E
D
,
E
are taken on the side
B
C
BC
B
C
of a triangle
A
B
C
ABC
A
B
C
such that
B
D
=
D
E
=
E
C
BD = DE = EC
B
D
=
D
E
=
E
C
. If
∠
B
A
D
=
x
\angle BAD = x
∠
B
A
D
=
x
,
∠
D
A
E
=
y
\angle DAE = y
∠
D
A
E
=
y
,
∠
E
A
C
=
z
\angle EAC = z
∠
E
A
C
=
z
, then the value of
sin
(
x
+
y
)
sin
(
y
+
z
)
sin
x
sin
z
\frac{\sin(x+y) \sin(y+z)}{\sin x \sin z}
s
i
n
x
s
i
n
z
s
i
n
(
x
+
y
)
s
i
n
(
y
+
z
)
is equal to a. 1 b. 2 c. 4 d. None of these
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