Answer :

We are given that,

…(i)


We need to find the value of x.


Using the property of inverse trigonometry,



Replace A by and B by .



Putting this value in equation (i),




Taking tangent on both sides,



Using the property of inverse trigonometry,


tan(tan-1 A) = A



Cross-multiplying, we get



Simplifying the equation in order to find the value of x,



Let us cancel the denominator from both sides of the equation.


x(x + 1) + (x – 1)(x – 1) = -7[x(x – 1) – (x + 1)(x – 1)]


x2 + x + (x – 1)2 = -7[x2 – x – (x + 1)(x – 1)]


Using the algebraic identity,


(a – b) = a2 + b2 – 2ab


And, (a + b)(a – b) = a2 – b2


x2 + x + x2 + 1 – 2x = -7[x2 – x – (x2 – 1)]


2x2 – x + 1 = -7[x2 – x – x2 + 1]


2x2 – x + 1 = -7[1 – x]


2x2 – x + 1 = -7 + 7x


2x2 – x – 7x + 1 + 7 = 0


2x2 – 8x + 8 = 0


2(x2 – 4x + 4) = 0


x2 – 4x + 4 = 0


We need to solve the quadratic equation to find the value of x.


x2 – 2x – 2x + 4 = 0


x(x – 2) – 2(x – 2) = 0


(x – 2)(x – 2) = 0


x = 2 or x = 2


Hence, x = 2.

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