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UPSC CDS Trigonometric Ratios and Trigonometric Identities Questions
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© examsnet.com
Question : 1
Total: 107
If
cos
2
+
cos
x
=
1
,
then what is the value of
sin
12
x
+
3
sin
10
x
+
3
sin
8
x
+
sin
6
x
?
[2019 CDS-II]
1
2
4
8
Validate
Solution:
We have
cos
2
x
+
cos
x
=
1
⇒
cos
x
=
1
−
cos
2
x
=
sin
2
x
sin
12
x
+
3
sin
10
x
+
3
sin
8
x
+
sin
6
x
⇒
cos
6
x
+
3
cos
5
x
+
3
cos
4
x
+
cos
3
x
⇒
(
cos
2
x
)
3
+
3
(
cos
2
x
)
2
(
cos
x
)
+
3
(
cos
2
x
)
(
cos
x
)
2
+
(
cos
x
)
3
⇒
(
cos
2
x
+
cos
x
)
2
⇒
1
2
=
1
© examsnet.com
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