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Byju's Answer
Standard XII
Mathematics
Theorems for Differentiability
Write the equ...
Question
Write the equation of a tangent to the graphs of the following curves at the indicated points
y
=
sin
2
x
at the point
x
=
π
12
.
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Solution
To find : - equation of a tangent of
y
=
sin
2
x
at
x
=
π
12
y
=
sin
(
2
x
)
at
x
=
π
12
y
=
sin
(
2
π
12
)
=
sin
π
6
=
1
2
Now,
y
′
=
2
cos
2
x
at
x
=
π
12
y
′
=
2
cos
(
π
12
)
=
2
cos
π
6
=
2
√
3
2
=
√
3
∴
s
l
o
p
e
=
m
=
√
3
Use point - slope form
(
y
−
y
0
)
=
m
(
x
−
x
0
)
where
x
0
=
π
12
,
y
0
=
1
2
,
m
=
√
3
(
y
−
1
2
)
=
√
3
(
x
−
π
12
)
y
=
√
3
x
−
√
3
π
12
+
1
2
=
√
3
x
+
1
2
(
−
√
3
π
6
+
1
)
.
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0
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