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TS EAMCET 19-July-2022 Shift 2 Solved Paper
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© examsnet.com
Question : 8
Total: 160
If
−
i
and
α
are the roots of the equation
i
z
2
−
2
(
i
+
1
)
z
+
(
2
−
i
)
=
0
,
tan
θ
=
−
1
2
and
θ
∈
4
th
quadrant, then
5
3
cos
6
θ
=
-117
-44
117
44
Validate
Solution:
Given,
i
z
2
−
2
(
i
+
1
)
z
+
(
2
−
i
)
=
0
∴
−
i
and
α
are the roots of above equation.
−
i
×
α
=
2
−
i
i
⇒
α
=
2
−
i
−
i
2
⇒
α
=
2
−
i
Clearly,
tan
θ
=
−
1
2
,
γ
=
√
5
s
i
n
θ
=
−
1
√
5
,
cos
θ
=
2
√
5
[ ∵ from the polar form ]
cos
2
θ
=
cos
2
θ
−
s
i
n
2
θ
=
4
5
−
1
5
=
3
5
cos
6
θ
=
4
cos
3
2
θ
−
3
cos
2
θ
=
4
(
3
5
)
3
−
3
×
3
5
=
108
125
−
9
5
=
108
−
225
125
=
−
117
125
∴
5
3
cos
6
θ
=
5
3
x
−
(
117
125
)
=
−
117
.
© examsnet.com
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