Q. 143.9( 9 Votes )

# Prove that: tan<s

Answer :

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 .

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