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Question

# The set of values of x in [0,2π] for which f(x)=√sinx−cosx is defined is

A
[0,π4]U [5π4,2π]
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B
[π4,3π4]
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C
[π4,5π4]
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D
[π3,3π2]
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Solution

## The correct option is C [π4,5π4]f(x)=√sinx−cosx is defined iff quantity inside square root is non negative. ⇒sinx−cosx>0 ⇒sinx>cosx ⇒ Set of values of x for which graph of y=sinx is above the graph of y=cosx in [0,2π]. As sinx,cosx are fundamental functions whose graphs are given by and now we need to find the set of x for which sinx>cosx from the graph From the above graph, we can conclude that x∈[π4,5π4]

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