The set of values of x satisfying [tan−1x]+[cot−1x]=2 where [.] is greatest integer function is
ϕ
[cot−1x]=0,1,2,3,[tan−1x]=−2,−1,0,1
Case(i)[cot−1x]=[tan−1x]=1
x∈(cot2,cot1], & x∈[tan1,∞)
∴x∈ϕ as cot 1 <tan 1
(ii) [cot−1x]=3, [tan−1x]=−1
x∈(−∞,cot3], x∈[−tan1,0]
∴x∈ϕascot3<−tan1
(iii) [cot−1x]=2, [tan−1x]=0
x∈(cot3,cot2],x∈[0,tan1)
x∈ ϕ as cot 2 < 0
So no solution.