Q.

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
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