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Mathematics
Problem
The angle made by the tangent of the curve
x
=
a
(
t
+
sin
t
cos
t
)
x = a(t + \sin t \cos t)
x
=
a
(
t
+
sin
t
cos
t
)
,
y
=
a
(
1
+
sin
t
)
2
y = a(1 + \sin t)^2
y
=
a
(
1
+
sin
t
)
2
with the
x
x
x
-axis at any point on it is (a)
1
4
(
π
+
2
t
)
\frac{1}{4}(\pi + 2t)
4
1
(
π
+
2
t
)
(b)
1
−
sin
t
cos
t
\frac{1 - \sin t}{\cos t}
c
o
s
t
1
−
s
i
n
t
(c)
1
4
(
2
t
−
π
)
\frac{1}{4}(2t - \pi)
4
1
(
2
t
−
π
)
(d)
1
+
sin
t
cos
2
t
\frac{1 + \sin t}{\cos 2t}
c
o
s
2
t
1
+
s
i
n
t
(a)
1
4
(
π
+
2
t
)
\frac{1}{4}(\pi + 2t)
4
1
(
π
+
2
t
)
(b)
1
−
sin
t
cos
t
\frac{1 - \sin t}{\cos t}
c
o
s
t
1
−
s
i
n
t
(c)
1
4
(
2
t
−
π
)
\frac{1}{4}(2t - \pi)
4
1
(
2
t
−
π
)
(d)
1
+
sin
t
cos
2
t
\frac{1 + \sin t}{\cos 2t}
c
o
s
2
t
1
+
s
i
n
t
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