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Mathematics
The equation tan 4x-2 sec 2x+a2=0 will have atleast one solution, if
Q. The equation
tan
4
x
−
2
sec
2
x
+
a
2
=
0
will have atleast one solution, if
1380
213
Jharkhand CECE
Jharkhand CECE 2012
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A
∣
a
∣
≤
4
B
∣
a
∣
≤
2
C
∣
a
∣
≤
3
D
∣
a
∣
≤
2
Solution:
tan
4
x
−
2
sec
2
x
+
a
2
=
0
⇒
tan
4
x
−
2
(
1
+
tan
2
x
)
+
a
2
=
0
⇒
tan
4
x
−
2
tan
2
x
+
1
=
3
−
a
2
⇒
(
tan
2
x
−
1
)
2
=
3
−
a
2
⇒
3
−
a
2
≥
0
⇒
a
2
≤
3
⇒
∣
a
∣
≤
3