The set of all x in (−π,π) satisying |4cosx−1|<√5 is
A
(−π,−4π5)∪(4π5,π)
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B
(−4π5,−π5)∪(π5,4π5)
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C
(−3π5,−π5)∪(π5,3π5)
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D
(−π,−π5)∪(π5,3π5)
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Solution
The correct option is C(−3π5,−π5)∪(π5,3π5) −√5<4cosx−1<√5,(1−√5)4<cosx<(1+√5)4
Here in (−π,π) cos(±π5)=(1+√5)4cos(±3π5)=(1−√5)4
From the graph x∈(−3π5,−π5)∪(π5,3π5)