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Question

The set of values of x satisfying [tan1x]+[cot1x]=2 where [.] is greatest integer function is


A

(cot 3, cot 2)

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B

(cot 3, -cot 1)

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C

(cot 3, 0)

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D

ϕ

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Solution

The correct option is D

ϕ


[cot1x]=0,1,2,3,[tan1x]=2,1,0,1

Case(i)[cot1x]=[tan1x]=1

x(cot2,cot1], & x[tan1,)

xϕ as cot 1 <tan 1

(ii) [cot1x]=3, [tan1x]=1

x(,cot3], x[tan1,0]

xϕascot3<tan1

(iii) [cot1x]=2, [tan1x]=0

x(cot3,cot2],x[0,tan1)

x ϕ as cot 2 < 0

So no solution.


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