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If x and y are positive and xygt1, then ...

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))`

Text Solution

Verified by Experts

The correct Answer is:
B
`tan^(-1)x+tan^(-1)y=tan^(-1)[(x+y)/(1-xy)], "where xy" lt 1`
And if `x lt 0, y lt 0 and xy gt 1`, then
`tan^(-1)x + tan^(-1)y = pi + tan^(-1)((x+y)/(1-xy))`
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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
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    3
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    C
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  • If x + y + z=xyz and x,y,z gt 0 , then the value of tan^(-1)x + tan^(-1)y + tan^(-1)z is equal to

    A
    `pi//2`
    B
    `pi//4`
    C
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    D
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