give the value of tan(arctan x+1/x-1+arctanx-1/x)

To calculate the value of tan(arctan x+1/x-1+arctanx-1/x), we can use trigonometric identities to simplify the expression. First, let's break down the given expression step by step:

Step 1: arctan x + 1/x - 1
To calculate this expression, we can use the following identity:
tan(arctan a) = a
So, tan(arctan x) = x.

Therefore, arctan x + 1/x - 1 simplifies to x + 1/x - 1.

Step 2: arctan x - 1/x
Similarly, applying the same identity, tan(arctan a) = a, we have:
tan(arctan x - 1/x) = x - 1/x.

Step 3: tan(x + 1/x - 1 + x - 1/x)
Now, substituting the values derived in step 1 and step 2, we get:
tan(x + 1/x - 1 + x - 1/x) = tan(2x).

Step 4: Finding the value of tan(2x)
To calculate tan(2x), we can use the following identity:
tan(2x) = (2 tan(x))/(1 - tan^2(x))

Therefore, tan(2x) = (2 tan(x))/(1 - tan^2(x))

So, the expression tan(arctan x+1/x-1+arctanx-1/x) simplifies to (2 tan(x))/(1 - tan^2(x)).