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Question

Find the domain of the following function:
f(x)= cosec1[1+sin2x], where [] denotes the greatest integer function

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Solution

Given function is, f(x)=cosec1[1+sin2x]
For this function to be defined,
[1+sin2x]1
[1+sin2x]1, (Since [1+sin2x]>0)
1+[sin2x]1
[sin2x]0
Clearly this inequality is true for all real number
Hence, the domain is xϵR

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