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Question

Let f(x)=cot(5+3x)(cot(5)+cot(3x))cot3x+1, the domain is

A
R{nπ3},nI
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B
(2n+1)π6,nI
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C
R{nπ3,nπ53},nI
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D
R{nπ53},nI
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Solution

The correct option is A R{nπ3},nI
Let,f(x)=cot(5+3x)(cot(5)+cot(3x))cot3x+1
f(x)=(cot5cot3x1cot5+cot3x)(cot5+cot3x)cot3x+1=cot5cot3x1cot3x+1=cot5cot3xcot3xcot5cot3x=cot3xcot5cot3x=0cot3x=0x=R{nπ3},nϵI

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