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WBJEE 2012 Math Solved Paper
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© examsnet.com
Question : 48
Total: 80
Let p, q and r be the sides opposite to the angles P,Q and R, respectively in a ΔPQR. Then,
2
p
r
sin
(
P
−
Q
+
R
2
)
equals
p
2
+
q
2
+
r
2
p
2
+
r
2
−
q
2
q
2
+
r
2
−
p
2
p
2
+
q
2
−
r
2
Validate
Solution:
In ΔPQR,
P
+
Q
+
R
=
180
°
∴
2
p
r
sin
(
P
−
Q
+
R
2
)
=
2
p
r
sin
180
∘
−
Q
−
Q
2
=
2
p
r
sin
(
90
∘
−
Q
)
=
2
p
r
cos
Q
(
In
∆
P
Q
R
cos
Q
=
p
2
+
r
2
−
q
2
2
p
r
)
=
2
p
r
(
p
2
+
r
2
−
q
2
2
p
r
)
=
p
2
+
r
2
−
q
2
© examsnet.com
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