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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