Prove that: tan^-1 (1) + tan^-1 (2) + tan^-1 (3) = π.

OR

If , find the value of x.

To Prove: tan^-1 (1) + tan^-1 (2) + tan^-1 (3) = π

Proof: It is of the form,

tan^-1 (A) + tan^-1 (B) + tan^-1 (C)

where, A = 1

B= 2

C = 3

We know the formula,

Here,

A = 1

B = 2

AB = 1 × 2

⇒ AB = 2

If AB > 1, then we must use the following formula

Hence, proved.

OR

We are given that,

We need to find the value of x.

We know the formula,

Just replace A by and B by , we get

We know that, (x – 2)(x + 2) = x² – 4 and (x – 1)(x + 1) = x² – 1

Therefore,

But, according to the question:

So, this means that Right Hand Sides of both the equations are equal.

That is,

Taking tangent of both sides,

⇒ 2x² – 4 = -3 × 1

⇒ 2x² – 4 = -3

⇒ 2x² = 4 – 3

⇒ 2x² = 1

Thus, the value of x is .