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Question

The number of real solutions of
tan1x(x+1)+sin1x2+x+1=π2 is

 [IIT 1999]


  1. Two

  2. Infinite

  3. Zero

  4. One


Solution

The correct option is A

Two


tan1x(x+1)+sin1x2+x+1=π2
tan1x(x+1) is defined when
x(x+1)0...........(i)
sin1x2+x+1 is defined when
0x(x+1)+11 or  x(x+1)0.......(ii)
From (i) and (ii), x(x + 1) = 0
or x = 0 and - 1.
Hence number of solution is 2.

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