The numbers 3^(2sin2x-1),14, 3^(4-2sin2x) form first three terms of an AP then x=
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consider that if there are three terms in an AP a,b,c then b-a=c-b
there fore 2b=a+c
there fore 2b=a+c
Answered by
0
Answer:
Since the numbers are in A.P.
∴
28
=
3
2
s
i
n
2
θ
−
1
+
3
4
−
2
s
i
n
2
θ
⇒
28
=
9
s
i
n
2
θ
3
+
81
9
s
i
n
2
θ
Let
x
=
9
s
i
n
2
θ
Hence,
x
2
−
84
x
+
243
=
0
⇒
(
x
−
81
)
(
x
−
3
)
=
0
∴
x
=
81
or 3
∴
x
=
9
s
i
n
2
θ
=
81
,
3
or
9
2
,
9
1
/
2
∴
s
i
n
2
θ
=
2
or 1/2
Since
s
i
n
2
θ
cannot be greater than 1 so we choose
s
i
n
2
θ
=
1
2
Hence the terms in A.P. are
3
0
,
14
,
27
i.e. 1, 14, 27.
∴
T
5
=
a
+
4
d
=
1
+
4
×
13
=
53
Step-by-step explanation:
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