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Byju's Answer
Standard XII
Mathematics
Conditional Identities
If cos x=12 a...
Question
If
cos
x
=
1
2
a
+
1
a
,
and
cos
3
x
=
λ
a
3
+
1
a
3
, then
λ
=
(a)
1
4
(b)
1
2
(c) 1
(d) none of these
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Solution
(b)
1
2
Given
:
cos
x
=
1
2
a
+
1
a
cos
3
x
=
λ
a
3
+
1
a
3
Now
,
cos
3
x
=
1
8
a
3
+
1
a
3
+
3
a
1
a
a
+
1
a
⇒
cos
3
x
=
1
8
a
3
+
1
a
3
+
3
×
2
cos
x
∵
cos
x
=
1
2
a
+
1
a
⇒
cos
3
x
=
1
8
cos
3
x
λ
+
6
cos
x
⇒
cos
3
x
=
1
8
4
cos
3
x
-
3
cos
x
λ
+
6
cos
x
⇒
cos
3
x
=
4
cos
3
x
8
λ
-
3
cos
x
8
λ
+
6
cos
x
8
On
comparing
the
powers
of
cos
3
x
on
both
sides
,
we
get
1
=
4
8
λ
⇒
λ
=
1
2
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