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Tardigrade
Question
Mathematics
If 2y cos θ = x sin θ and 2x sec θ - y cosec θ = 3, then x2 + 4y2 =
Q. If
2
y
cos
θ
=
x
s
in
θ
an
d
2
x
sec
θ
−
y
cosec
θ
=
3
,
then
x
2
+
4
y
2
=
1690
195
Trigonometric Functions
Report Error
A
4
15%
B
-4
15%
C
±4
58%
D
None of these
13%
Solution:
Given that
2
y
cos
θ
=
x
s
in
θ
...
(
i
)
and
2
x
sec
θ
−
y
cosec
θ
=
3
...
(
ii
)
⇒
cos
θ
2
x
−
s
in
θ
y
=
3
⇒
2
x
s
in
θ
−
y
cos
θ
−
3
s
in
θ
cos
θ
=
0
...
(
iii
)
Solving
(
i
)
and
(
iii
)
, we get
y
=
s
in
θ
and
x
=
2
cos
θ
Now,
x
2
+
4
y
2
=
4
co
s
2
θ
+
4
s
i
n
2
θ
=
4
(
co
s
2
θ
+
s
i
n
2
θ
)
=
4