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Mathematics
Problem
Let
x
=
x
(
y
)
x = x(y)
x
=
x
(
y
)
be the solution of the differential equation
y
=
(
x
−
y
d
x
d
y
)
sin
(
x
y
)
,
y
>
0
and
x
(
1
)
=
π
2
y = \left( x - y \frac{dx}{dy} \right) \sin\left(\frac{x}{y}\right),\; y > 0 \text{ and } x(1) = \frac{\pi}{2}
y
=
(
x
−
y
d
y
d
x
)
sin
(
y
x
)
,
y
>
0
and
x
(
1
)
=
2
π
Then
cos
(
x
(
2
)
)
\cos(x(2))
cos
(
x
(
2
))
is equal to : [NCERT : P L-306 | Jan. 23, 2025 (II)] (a)
1
−
2
(
log
e
2
)
2
1 - 2(\log_e 2)^2
1
−
2
(
lo
g
e
2
)
2
(b)
2
(
log
e
2
)
2
−
1
2(\log_e 2)^2 - 1
2
(
lo
g
e
2
)
2
−
1
(c)
2
(
log
e
2
)
−
1
2(\log_e 2) - 1
2
(
lo
g
e
2
)
−
1
(d)
1
−
2
(
log
e
2
)
1 - 2(\log_e 2)
1
−
2
(
lo
g
e
2
)
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