Home
Class 12
MATHS
Solve : tan^(-1)(x-1)/(x-2)+tan^(-1)(x+1...

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

Text Solution

Verified by Experts

The correct Answer is:
`x = sqrt((5)/(2))`
`tan^(-1).(x -1)/(x + 2) + tan^(-1).(x + 1)/(x + 2) = (pi)/(4)`
`rArr tan^(-1) [((x -1)/(x + 2) + (x + 1 )/(x + 2))/(1 - ((x -1)/(x + 2)) ((x +1)/(x + 2)))] = (pi)/(4)`
`rArr [(2x (x + 2))/(x^(2) + 4 + 4x -x^(2) + 1)] = tan.(pi)/(4)`
`rArr (2x (x + 2))/(4x + 5) = 1`
`rarr 2x^(2) + 4x = 4x + 5`
`:. x = +- sqrt((5)/(2))`
But for `x = -sqrt5//2`, L.H.S. is negative
Hence, `x = sqrt(5//2)`
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 7.6|9 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Single)|80 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 7.4|12 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise JEE Previous Year|20 Videos

  • JEE 2019

    CENGAGE|Exercise Chapter 10|9 Videos

Similar Questions

Explore conceptually related problems

Solve : tan^(-1)((x+1)/(x-1)) + tan^(-1)( (x-1)/(x)) = pi + tan^(-1) (-7)

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

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

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

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

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

Solve: tan^(-1)((x-1)/(x+1))+tan^(-1)((2x-1)/(2x+1))=tan^(-1)((23)/(36))

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