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If tan ^(-1) x + tan ^(-1) y + tan ^(-1)...

If `tan ^(-1) x + tan ^(-1) y + tan ^(-1) z = (pi)/(2),` then ` xy + yz+zx` is equal to

A

0

B

`1//2`

C

`1//3`

D

1

Text Solution

Verified by Experts

The correct Answer is:
D
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FIITJEE-MATHEMATICS -OBJECTIVE
  1. The equations of the sided of a triangle are x+y-5=0,x-y+1=0, and x+y-...

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  2. If P=(x , y),F1=(3,0),F2=(-3,0), and 16 x^2+25 y^2=400 , then P F1+P F...

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  3. If tan ^(-1) x + tan ^(-1) y + tan ^(-1) z = (pi)/(2), then xy + yz+z...

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  4. The number of tangents and normals to the hyperbola x^2/16-y^2/25 = 1 ...

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  5. If xy + yz + zx = 1 then (sum (x + y)/(1 - xy)=

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  6. The equatin 2x = (2n +1)pi (1 - cos x) , (where n is a positive intege...

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  7. If xy = m^(2) -4 be a reactangular hyperbola whose branches lies only...

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  8. Number of points on hyperbola (x ^(2))/(a ^(2)) - (y ^(2))/(b ^(2)) =1...

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  9. In a triangle ABC, A - B =120 ^(@) and R = 8r, then the value of cos C...

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  10. x ^(2) (lamda ^(2) - 4 lamda + 3) +y ^(2) (lamda ^(2) - 6 lamda +5) =1...

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  11. For all real values of a and b lines (2a + b) x + (a + 3b) y + (b - 3a...

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  12. A line of slope lambda(0<lambda<1) touches the parabola y+3x^2=0 at Pd...

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  13. Normals at two points (x1y1)a n d(x2, y2) of the parabola y^2=4x meet ...

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  14. If A (3,1) and B (-5,7) are any two given points, If P is a point one ...

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  15. Let f (x) = sin x - ax and g (x) - sin x - bx, where 0 lt a,b, lt 1 Su...

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  16. If sin ^(-1)((1 - x ^(2))/(1 + x ^(2)))+ cos ^(-1) ((2x )/(1 +x ^(2)))...

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  17. From a point P outside a circle with centre at C, tangents PA and PB a...

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  18. the equation of the radical axis of the two circles 7x^2+7y^2-7x+14y+...

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  19. Point on the curve y ^(2) = 4 (x -10) which is nearest to the line x ...

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  20. If (t,0) is point on diameter of circle x ^(2) + y ^(2) =4, then the e...

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