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UPSC NDA 2 2016 Mathematics Solved Paper
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© examsnet.com
Question : 45
Total: 120
If
x
cos
θ
+
y
sin
θ
=
z
, then what is the value of
(
x
sin
θ
−
y
cos
θ
)
2
?
[NDA II 2016]
x
2
+
y
2
−
z
2
x
2
−
y
2
−
z
2
x
2
−
y
2
+
z
2
x
2
+
y
2
+
z
2
Validate
Solution:
Here
z
=
x
cos
θ
+
y
sin
θ
z
2
=
x
2
cos
2
θ
+
y
2
sin
2
θ
+
2
x
y
sin
θ
cos
θ
⇒
2
x
y
sin
θ
cos
θ
=
z
2
−
x
2
cos
2
θ
−
y
2
sin
2
θ
Let,
L
=
(
x
sin
θ
−
y
cos
θ
)
2
⇒
L
=
x
2
sin
2
θ
+
y
2
cos
2
θ
−
2
x
y
sin
θ
cos
θ
⇒
L
=
x
2
sin
2
θ
+
y
2
cos
2
θ
−
[
z
2
−
x
2
cos
2
θ
−
y
2
sin
2
θ
]
⇒
L
=
x
2
[
sin
2
θ
+
cos
2
θ
]
+
y
2
[
sin
2
θ
+
cos
2
θ
]
−
z
2
⇒
L
=
x
2
+
y
2
−
z
2
© examsnet.com
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