The number of Solutions of the equation Tan−1x−1+Tan−1x+Tan−1x+1=Tan−13xis /are
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a
4
b
3
c
2
d
1
answer is B.
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Detailed Solution
We have Tan-1x-1+Tan-1x+Tan-1x+1=Tan-13x⇒Tan−1x−1+Tan−1x+1=Tan−13x−Tan−1x⇒Tan-1x-1+x+11-x-1x+1=Tan-13x-x1+3xx ⇒2x2-x2=2x1+3x2 ⇒2x1+3x2-2+x2=0 ⇒x=0,x2=14 ⇒x=0, x=±12