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Byju's Answer
Standard XII
Mathematics
Range of Trigonometric Expressions
If p =4 cos x...
Question
If
p
=
4
cos
(
x
−
π
3
)
+
3
√
3
sin
x
,
then the maximum value of
[
p
]
is
(where [.] denotes greatest integer function)
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Solution
cos
(
x
−
π
3
)
=
cos
x
cos
π
3
+
sin
x
sin
π
3
⇒
cos
(
x
−
π
3
)
=
1
2
cos
x
+
√
3
2
sin
x
So,
p
=
4
(
1
2
cos
x
+
√
3
2
sin
x
)
+
3
√
3
sin
x
⇒
p
=
2
cos
x
+
5
√
3
sin
x
⇒
p
max
=
√
2
2
+
(
5
√
3
)
2
=
√
79
⇒
[
p
]
max
=
8
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2
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Range of Trigonometric Expressions
Standard XII Mathematics
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