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Byju's Answer
Standard XII
Mathematics
Secant of a Curve y =f(x)
Find the slop...
Question
Find the slope of the tangent and normal to the curve
y
=
(
sin
2
x
+
cot
x
+
2
)
2
at
x
=
π
2
.
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Solution
We have,
y
=
(
sin
2
x
+
cot
x
+
2
)
2
On differentiating both sides w.r.t. x, we get,
d
y
d
x
=
2
(
sin
2
x
+
cot
x
+
2
)
d
d
x
(
sin
2
x
+
cot
x
+
2
)
d
y
d
x
=
2
(
sin
2
x
+
cot
x
+
2
)
(
2
cos
2
x
−
c
o
s
e
c
2
x
)
Therefore,
(
d
y
d
x
)
x
=
π
/
2
=
sin
π
+
cot
π
2
+
2
=
2
[
0
+
0
+
2
]
[
−
2
−
1
]
=
−
12
Therefore, slope of tangent = -12
And, slope of normal
=
1
12
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0
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Secant of a Curve y =f(x)
Standard XII Mathematics
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