tanh-1x=
12logx+1x-1
12logx-1x+1
12log1-x1+x
12log1+x1-x
Explanation for the correct answer
Solving the given trigonometric expression
Given, tanh-1x
Therefore,
y=tanh-1x⇒x=tanhy=ey-e-yey+e-y∵tanhy=ey-e-yey+e-y=e2y-1e2y+1
This gives:
xe2y+1=e2y-1⇒x-1e2y+x+1=0⇒e2y=-(1+x)x-1=1+x1-x
Taking logarithm on both sides:
2y=log1+x1-x⇒y=12log1+x1-x
Therefore, the value of tanh-1x is 12log1+x1-x.
Hence, the correct answer is Option (D).
Factorise: x4-1