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Byju's Answer
Standard XII
Mathematics
Properties of Inequalities
Write the sol...
Question
Write the solution set of the equation
2
cos
x
+
1
4
cos
x
+
5
=
0
in the interval [0, 2π].
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Solution
Given:
(
2
cos
x
+
1
)
(
4
cos
x
+
5
)
=
0
Now,
2
cos
x
+
1
=
0
or
4
cos
x
+
5
=
0
⇒
cos
x
=
-
1
2
or
cos
x
=
-
5
4
cos
x
=
-
5
4
is not possible.
Thus, we have:
cos
x
=
-
1
2
⇒
cos
x
=
cos
2
π
3
⇒
x
=
2
n
π
±
2
π
3
By putting n = 0 and n = 1 in the above equation, we get:
x
=
2
π
3
or
x
=
4
π
3
in the interval
0
,
2
π
For the other value of n, x will not satisfy the given condition.
∴
x
=
2
π
3
and
4
π
3
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