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TS EAMCET 11-Sep-2020 Shift 1 Solved Paper
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© examsnet.com
Question : 7
Total: 160
For some
a
,
b
,
c
∊
R
, if
s
i
n
5
θ
=
a
c
o
s
4
θ
s
i
n
θ
+
b
c
o
s
2
θ
s
i
n
3
θ
+
c
s
i
n
5
θ
, then
a
b
c
=
-10
10
0
-50
Validate
Solution:
Given
sin
5
θ
=
a
cos
4
θ
sin
θ
+
b
cos
2
θ
sin
3
θ
+
c
sin
5
θ
at
θ
=
π
2
, we get
1
=
0
+
0
+
c
⇒
c
=
1
....(i)
at
θ
=
π
4
, we get
−
1
√
2
=
a
1
4
×
1
√
2
+
b
1
2
1
2
√
2
+
1
4
√
2
⇒
−
1
=
a
4
+
b
4
+
1
4
⇒
a
+
b
=
−
5
.....(ii)
at
θ
=
π
3
, we get
−
√
3
2
=
a
1
16
×
√
3
2
+
b
1
4
3
√
3
8
+
9
√
3
32
⇒
−
1
=
a
16
+
3
b
16
+
9
16
⇒
a
+
3
b
=
−
25
...(iii)
From Eqs. (ii) and (iii), we get
b
=
−
10
and
a
=
5
∴
a
b
c
=
−
50
© examsnet.com
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