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KEAM 2019 Math Paper
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© examsnet.com
Question : 65
Total: 121
Number of values of
a
in the interval
[
−
π
,
0
]
which satisfy
sin
a
+
2
a
∫
a
cos
2
x
d
x
=
0
are
0
1
2
3
infinite
Validate
Solution:
sin
a
+
[
sin
2
x
2
]
a
2
a
=
0
sin
a
+
sin
4
a
−
sin
2
a
2
=
0
⇒
2
sin
a
+
sin
4
a
−
sin
2
a
=
0
⇒
2
sin
a
+
2
cos
3
a
sin
a
=
0
⇒
2
sin
a
(
1
+
cos
3
a
)
=
0
⇒
sin
a
(
1
+
cos
3
a
)
=
0
⇒
sin
a
=
0
,
cos
3
a
=
−
1
∴
a
=
0
or
3
a
=
−
π
,
−
3
π
a
=
−
π
3
,
−
π
,
0
© examsnet.com
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