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# If Tan^(-1) (X-1)/(X - 2) + Tan^(-1) (X + 1)/(X + 2) = Pi/4 Then Find the Value Of X. - CBSE (Science) Class 12 - Mathematics

ConceptProperties of Inverse Trigonometric Functions

#### Question

if tan^(-1)  (x-1)/(x - 2) + tan^(-1)  (x + 1)/(x + 2) = pi/4 then find the value of x.

#### Solution

tan^(-1)  (x - 1)/(x - 2) + tan^(-1)  (x + 1)/(x + 2) = pi/4

=> tan^(-1) [((x-1)/(x-2) + (x +1)/(x +2))/(1 - ((x-1)/(x-2))((x + 1)/(x+2)) ]] = pi/4     [tan^(-1) x + tan^(-1) y = tan^(-1)   (x+y)/(1-xy)]

=> tan^(-1) [((x-1)(x+2)+(x+1)(x-2))/((x + 2)(x-2) - (x - 1)(x + 1)]] = pi/4

=> tan^(-1) [(x^2 + x - 2 + x^2 -  x- 2)/(x^2 - 4 - x^2 + 1)] = pi/4

=> tan^(-1) [(2x^2 - 4)/(-3)] = pi/4

=> tan[tan^(-1)  (4 - 2x^2)/3] = tan  pi/4

=> (4- 2x^2)/3  = 1

=> 4  - 2x^2 = 3

=> 2x^2 = 4 - 3 =1

=> x = +- 1/sqrt2

Hence, the value of x is  +- 1/sqrt2

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#### APPEARS IN

NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 2: Inverse Trigonometric Functions
Q: 15 | Page no. 48
Solution If Tan^(-1) (X-1)/(X - 2) + Tan^(-1) (X + 1)/(X + 2) = Pi/4 Then Find the Value Of X. Concept: Properties of Inverse Trigonometric Functions.
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