AP EAPCET 23-Aug-2021 Shift 1 Paper

tanh−1x−

1

2

loge(

1+x

1−x

)When x=1 identity does not hold as loge(

2

0

) will form.
At x=−1 also identity does not hold as loge(

0

−2

) will form and loge0 does not exist.
When x<−1 , then

1+x

1−x

becomes negative, then identity fails to exist.
When x>1 , then

1+x

1−x

becomes negative, then identity fails to exist.
∴ Identity valid only for x∈(−1,1) .