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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

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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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