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AP EAMCET Engineering 21 Apr 2019 Shift 1 Paper
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© examsnet.com
Question : 2
Total: 160
The maximum value of the function f (x) = tan
(
x
+
2
π
3
)
- tan
(
x
+
π
6
)
+ cos
(
x
+
π
6
)
in
[
−
5
π
12
,
−
π
3
]
is
11
√
2
6
11
√
3
6
3
1
Validate
Solution:
Consider the given function.
f
(
x
)
=
tan
(
x
+
2
π
3
)
−
tan
(
x
+
π
6
)
+
cos
(
x
+
π
6
)
So,
f
(
x
)
=
sin
π
2
cos
(
x
+
2
π
3
)
cos
(
x
+
π
6
)
+
cos
(
x
+
π
6
)
=
1
×
2
2
cos
(
x
+
2
π
3
)
cos
(
x
+
π
6
)
+
cos
(
x
+
π
6
)
=
cos
(
x
+
30
∘
)
−
2
cos
(
2
x
−
30
∘
)
Differentiate the above function with respect to x.
f
′
(
x
)
=
−
sin
(
x
+
30
∘
)
−
4
sin
(
2
x
−
30
∘
)
cos
2
(
2
x
−
30
∘
)
f
′
(
x
)
>
0
for all
−
75
∘
<
x
<
−
60
∘
f
max
at
x
=
−
60
∘
Find the value of the function.
f
(
−
60
∘
)
=
−
tan
(
60
∘
)
−
tan
(
−
30
∘
)
+
cos
(
−
30
∘
)
=
√
3
+
√
3
2
+
√
3
2
=
6
√
3
+
2
√
3
+
3
√
3
6
=
11
√
3
6
© examsnet.com
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