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Question

If y=2tan1x+sin12x1+x2 then

A
π/2<y<π/2
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B
3π/2<y<3π/2
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C
π<y<π
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D
π/4<y<π/4
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Solution

The correct option is C 3π/2<y<3π/2
Given y=2tan1x+sin12x1+x2

π2<tan1x<π2π<2tan1x<π ..(1)

we know that π2sin1θπ2

Here θ=2x1+x2

π2sin12x1+x2π2 ..(2)
Adding (1) and (2), we get
3π2<2tan1x+sin12x1+x2<3π2

3π2<y<3π2

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