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Byju's Answer
Standard X
Mathematics
Trigonometric Identities
If tanθ =a-...
Question
If
tan
θ
=
a
−
1
4
a
, then
sec
θ
−
tan
θ
equals
A
2
a
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B
1
2
a
,
2
a
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C
−
1
2
a
,
2
a
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D
−
2
a
,
1
2
a
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Solution
The correct option is
C
−
2
a
,
1
2
a
tan
θ
=
a
−
1
4
a
L
e
t
k
=
sec
θ
−
tan
θ
⇒
k
=
√
1
+
tan
2
θ
−
tan
θ
{
∵
sec
2
θ
=
1
+
tan
2
θ
}
⇒
k
=
√
1
+
(
a
−
1
4
a
)
2
−
a
+
1
4
a
⇒
k
=
√
(
a
+
1
4
a
)
2
−
a
+
1
4
a
=
±
(
a
+
1
4
a
)
−
a
+
1
4
a
∴
k
=
−
2
a
,
1
2
a
Ans: D
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