Home
Class 12
MATHS
If x and y are positive integer satisfyi...

If x and y are positive integer satisfying `tan^(-1)((1)/(x))+tan^(-1)((1)/(y))=(1)/(7)`, then the number of ordered pairs of (x,y) is

A

3

B

4

C

5

D

6

Text Solution

Verified by Experts

The correct Answer is:
D
`tan^(-1)((1)/(x))+tan^(-1)((1)/(y))=(1)/(7)`
`rArr tan^(-1)(((1)/(x)+(1)/(y))/(1-(1)/(xy)))=tan^(-1)((1)/(7))`
`rArr (x+y)/(xy-1)=(1)/(7)`
`rArr 7x+7y=xy-1`
`rArr (7-y)x=-7y-1`
`rArr x=(7y+1)/(y-7)=7+(50)/(y-7)`
Here, y = 8, 9, 12, 17, 32, 57 satisfy above equation.
Doubtnut Promotions Banner Mobile Dark
|

Similar Questions

Explore conceptually related problems

Find the value of tan^(-1)((x)/(y))-tan^(-1)((x-y)/(x+y))

Find the value of tan^(-1)((x)/(y))-tan^(-1)((x-y)/(x+y))

Knowledge Check

  • If x and y are positive integers such that tan^(-1)x+cot^(-1)y=tan^(-1)3 , then:

    A
    `x gt 2, y lt 2`
    B
    `x lt 3, y ge 2`
    C
    `x le 2, y le 7`
    D
    `x gt 2, y gt 7`

  • If x and y are positive and xygt1 , then what is tan^(-1)x+tan^(-1)y to?

    A
    `tan^(-1)((x+y)/(1-xy))`
    B
    `pi+tan^(-1)((x+y)/(1-xy))`
    C
    `pi-tan^(-1)((x+y)/(1-xy))`
    D
    `tan^(-1)((x-y)/(1-xy))`

  • If x and y are positive and xy gt 1, then what is tan^(-1)x + tan^(-1)y equal to ?

    A
    `tan^(-1)((x+y)/(1-xy))`
    B
    `pi + tan^(-1)((x+y)/(1-xy))`
    C
    `pi-tan^(-1)((x+y)/(1-xy))`
    D
    `tan^(-1)((x-y)/(1+xy))`

    • Similar Questions

    Explore conceptually related problems

    Formula for tan^(-1)(x)+-tan^(-1)(y)

    Tan^(-1)((x)/(y))-Tan^(-1)((x-y)/(x+y)) is equal to

    tan^(-1)x+tan^(-1)y=pi+tan^(-1)((x+y)/(1-xy))

    tan^(-1) ""x/y - tan^(-1) ""(x-y)/(x+y)=

    If 1/x+1/y=1/2007 where x lt y , then the number of positive integer pairs (x,y) is

    Home
    Profile