The set of points of continuity of the function y=12−cos2x contains in the interval
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a
[π4, 3π4]
b
[5π4, 7π4]
c
[21π4, 23π4]
d
All the above
answer is D.
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Detailed Solution
y=12−cos2x If is defined when 12−cos2x≥0 ⇒12≥cos2xi.e., 0≤cos2x≤12⇒−12≤cosx≤0,0≤cosx≤12⇒−12≤cosx≤12⇒x∈[π4,3π4],[5π4,7π4],[21π4,23π4]⇒x∈[2nπ-3π4,2nπ-π4] ∪ [2nπ+π4,2nπ+3π4], n∈zFrom all above