If –1 < x < 0 then tan–1x equals
π−cos−11−x2
sin−1x1+x2
−cot−11−x2x
cosec–1x
∵−1<x<0, ∴−π4<tan−1x<0
Let tan−1x=α⇒−π4<α<0
∴tanα=x,−π4<α<0
∴sinα=x1+x2⇒α=sin−1x1+x2
and, cosα=11+x2⇒cos(−α)=11+x2
where, 0<−α<π4⇒α=−cos−111+x2