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Byju's Answer
Standard XII
Mathematics
Orthocenter
The equation ...
Question
The equation of the normal to the curve y = x + sin x cos x at x = π/2 is
(a) x = 2
(b) x = π
(c) x + π = 0
(d) 2x = π
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Solution
(d) 2x = π
Given
:
y
=
x
+
sin
x
cos
x
On
d
ifferentiating both sides w.r.t.
x
,
we
get
d
y
d
x
=
1
+
cos
2
x
-
sin
2
x
Slope of the tangent=
d
y
d
x
x
=
π
2
=1+cos
2
π
2
-sin
2
π
2
=1-1=0
Slope of the normal,
m
=
-
1
0
When
x
=
π
2
,
y=
π
2
+cos
π
2
sin
π
2
=
π
2
Now
,
x
1
,
y
1
=
π
2
,
π
2
∴
Equation of the normal
=
y
-
y
1
=
m
x
-
x
1
⇒
y
-
π
2
=
-
1
0
x
-
π
2
⇒
x
=
π
2
⇒
2
x
=
π
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