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UPSC CDS Math Trigonometric Ratios and Trigonometric Identities Questions
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© examsnet.com
Question : 2
Total: 107
If 0 < 0 < 90°,
sin
θ
=
3
5
and
=
cot
θ
, then what is the value of
1
+
3
x
+
9
x
2
+
27
x
3
+
81
x
4
+
243
x
3
?
[2019 CDS-II]
941
1000
1220
1365
Validate
Solution:
If
0
<
θ
<
90
∘
,
then all the ratios will be positive.
Given that
sin
θ
=
3
5
⇒
x
=
cot
θ
=
√
csc
2
θ
−
1
=
√
25
9
−
1
=
4
3
⇒
3
x
=
4
S
o
1
+
3
x
+
9
x
2
+
27
x
3
+
81
x
4
+
243
x
5
⇒
1
+
3
x
+
(
3
x
)
2
+
(
3
x
)
3
+
(
3
x
)
4
+
(
3
x
)
5
⇒
1
+
4
+
4
2
+
4
3
+
4
4
+
4
5
⇒
4
6
−
1
4
−
1
⇒
4095
3
⇒
1365
© examsnet.com
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