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Test Index
KEAM 2011 Math Paper
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© examsnet.com
Question : 2 of 120
Marks:
+1
,
-0
The distance between the points
(
a
c
o
s
α
,
a
s
i
n
α
)
and
(
a
c
o
s
β
,
a
s
i
n
β
)
is
2
|
s
i
n
(
α
−
β
2
)
|
2
|
a
s
i
n
(
α
−
β
2
)
|
2
|
a
c
o
s
(
α
−
β
2
)
|
|
a
c
o
s
(
α
−
β
2
)
|
2
|
a
(
1
−
c
o
s
(
α
−
β
)
)
|
Validate
Solution:
Points
(
a
cos
α
,
a
sin
α
)
and
(
a
cos
β
,
a
sin
β
)
distance between the points
=
√
(
a
cos
α
−
a
cos
β
)
2
+
(
a
sin
α
−
a
sin
β
)
2
=
√
a
2
(
cos
2
α
+
cos
2
β
+
sin
2
α
+
sin
2
β
−
2
cos
α
⋅
cos
β
+
2
sin
α
⋅
sin
β
)
=
|
a
|
√
(
sin
2
α
+
cos
2
α
)
+
(
sin
2
β
+
cos
2
β
)
−
2
(
cos
α
⋅
cos
β
+
sin
α
⋅
sin
β
)
=
|
a
|
√
2
−
2
cos
(
α
−
β
)
=
|
a
|
√
2
√
1
−
cos
(
α
−
β
)
=
√
2
|
a
|
√
2
sin
2
(
α
−
β
)
2
=
|
a
|
√
2
√
2
|
sin
(
α
−
β
)
2
|
=
2
|
a
⋅
sin
(
α
−
β
)
2
|
© examsnet.com
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