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UPSC CDS Math Trigonometric Ratios and Trigonometric Identities Questions
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© examsnet.com
Question : 20
Total: 107
If
3
s
i
n
θ
+
5
c
o
s
θ
=
4
, then what is the value of
(
3
c
o
s
θ
−
5
s
i
n
θ
)
2
?
[2018 CDS-II]
9
12
16
18
Validate
Solution:
3
s
i
n
θ
+
5
c
o
s
θ
=
4
Now
(
3
cos
θ
−
5
sin
θ
)
2
Squaring both sides, we get:
(
3
sin
θ
+
5
cos
θ
)
2
=
4
2
⇒
9
sin
2
θ
+
25
cos
2
θ
+
30
sin
θ
cos
θ
=
16
⇒
9
(
1
−
cos
2
θ
)
+
25
(
1
−
sin
2
θ
)
+
30
sin
θ
cos
θ
=
16
⇒
9
−
9
cos
2
θ
+
25
−
25
sin
2
θ
+
30
sin
θ
cos
θ
=
16
⇒
−
9
cos
2
θ
−
25
sin
2
θ
+
30
sin
θ
cos
θ
=
−
18
⇒
9
cos
2
θ
+
25
sin
2
θ
−
30
sin
θ
cos
θ
=
18
⇒
(
3
cos
θ
−
5
sin
θ
)
2
=
18
© examsnet.com
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