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Question

If θ=sin1x+cos1xtan1x,1x<, then the smallest interval in which θ lies is

A
π2θ3π4
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B
0θπ4
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C
π4θ0
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D
π4θπ2
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Solution

The correct option is B 0θπ4
Given, θ=sin1x+cos1xtan1x
= π2 -tan1x because sin1x +cos1x = π2 = tan1(x)
θ=cot1x
Since, 1x<, therefore 0θ<π4

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