If a = xã then d equals
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Correct option is
C
−
a
3
3b
cosec
4
θcotθ
∵x=acosθ
⇒
dθ
dx
=−asinθ⟶(1)
and, y=bcosθ
⇒
dθ
dy
=bcosθ⟶(2)
also,
dx
dy
=
dθ
dx
dθ
dy
=
−asinθ
bcosθ
=−
a
b
cotθ
Now,
dx
2
d
2
y
=
dx
d
(
dx
dy
)
=
dx
d
(−
a
b
cotθ)
=
a
−b
(−cosec
2
θ)
dx
dθ
=
a
b
cosec
2
θ(
asinθ
−1
)(From(1))
=−
a
2
b
cosec
3
θ(sinx=
cosecx
1
)
again,
dx
3
d
3
y
=
dx
d
(
dx
2
d
2
y
)
=
dx
d
(−
a
2
b
cosec
3
θ)
=
a
3
−3b
cosec
4
θcotθ
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