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Byju's Answer
Standard XII
Mathematics
Geometric Mean
Let sin 2β ...
Question
Let
s
i
n
2
β
is the geometric mean between
s
i
n
α
and
c
o
s
α
, if
c
o
s
4
β
is equal to
λ
s
i
n
2
(
π
4
−
α
)
, then
λ
is
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Solution
s
i
n
2
β
=
√
s
i
n
α
.
c
o
s
α
c
o
s
4
β
=
1
−
2
s
i
n
2
2
β
=
1
−
2
s
i
n
α
.
c
o
s
α
=
(
s
i
n
α
−
c
o
s
α
)
2
=
2
s
i
n
2
(
α
−
π
4
)
=
2
s
i
n
2
(
π
4
−
α
)
⇒
λ
=
2
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