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UPSC NDA I 2017 Mathematics Solved Paper
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© examsnet.com
Question : 20
Total: 120
If
s
e
c
θ
−
c
o
s
e
c
θ
=
4
3
,then what is
(
s
i
n
θ
−
c
o
s
θ
)
equal to ?
[NDA I 2017]
−
2
only
1
2
only
Both
−
2
and
1
2
Neither
1
2
nor
−
2
Validate
Solution:
sin
θ
cosec
θ
=
4
3
⇒
sin
θ
−
cos
θ
sin
θ
cos
θ
=
4
3
⟶
(
sin
θ
−
cos
θ
)
2
(
sin
θ
cos
θ
)
2
=
16
9
⟹
1
−
2
sin
θ
cos
θ
sin
2
θ
cos
2
θ
=
16
9
Let
sin
θ
cos
θ
=
x
⇒
1
−
2
x
x
2
=
16
9
⇒
16
x
2
+
18
x
−
9
=
0
⇒
(
8
x
−
3
)
(
2
x
+
3
)
=
0
⇒
x
=
3
8
,
x
=
3
2
⇒
sin
θ
cos
θ
=
3
8
⇒
sin
θ
−
cos
θ
=
4
3
×
3
8
=
1
2
© examsnet.com
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