Home
Class 12
MATHS
If tan^(-1)x+tan^(-1)y+tan^(-1)z=pi/2,t ...

If `tan^(-1)x+tan^(-1)y+tan^(-1)z=pi/2,t h e n` (a) `x+y+z-x y z=0` (b) `x+y+z+x y z=0` (c) `x y+y z+z x+1=0` (d)`x y+y z+z x-1=0`

Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise JEE Previous Year|20 Videos

  • JEE 2019

    CENGAGE|Exercise Chapter 10|9 Videos

Similar Questions

Explore conceptually related problems

If tan^(-1)x+tan^(-1)y+tan^(-1)z=pi, show that x + y + z = xyz.

If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi,t h e n (a) x^2+y^2+z^2+x y z=0 (b) x^2+y^2+z^2+2x y z=0 (c) x^2+y^2+z^2+x y z=1 (d) x^2+y^2+z^2+2x y z=1

Prove that tan^(-1)x+tan^(-1)y+tan^(-1)z=tan^(-1)((x+y+z-xyz)/(1-xy-yz-zx))

If cot^(-1)x+cot^(-1)y+cot^(-1)z=pi/2,x , y , z >0a n dx y<1, then x+y+z is also equal to (a) 1/x+1/y+1/z (b) x y z (c) xy+yz+zx (d) none of these

Solve x + y = 7 , y + z = 4 , z + x = 1

IF sin^(-1) X+ sin^(-1) y+ sin^(-1) z= pi , then prove that x^4 +y^4+ z^4 +4x^2 y^2 z^2 = 2(x^2 y^2 +y^2 z^2+z^2x^2).

For 0

The determinant |x p+y x y y p+z y z0x p+y y p+z|=0 if x ,y ,z

Solve the system: x + y - 2z = 0, 2x - 3y + z = 0, 3x - 7y + 10z = 0, 6x - 9y + 10z = 0.

If cos^(-1) x + cos^(-1) y + cos ^(-1) z = pi and 0 lt x,y,z lt 1 show that x^(2) +y^(2) +z^(2) +2xyz = 1

CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. The number of solutions of the equation tan^(-1)(1+x)+tan^(-1)(1-x)=pi...

    Text Solution

    |

  2. If x , y , z are natural numbers such that cot^(-1)x+cot^(-1)y=cot^(-1...

    Text Solution

    |

  3. If tan^(-1)x+tan^(-1)y+tan^(-1)z=pi/2,t h e n (a) x+y+z-x y z=0 (b) ...

    Text Solution

    |

  4. If x^2+y^2+z^2=r^2,t h e ntan^(-1)((x y)/(z r))+tan^(-1)((y z)/(x r))+...

    Text Solution

    |

  5. If cot^(-1)x+cot^(-1)y+cot^(-1)z=pi/2,x , y , z >0a n dx y<1, then x+y...

    Text Solution

    |

  6. If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi,t h e n (a)x^2+y^2+z^2+x y z=0 ...

    Text Solution

    |

  7. If 0 < cos^(-1)x < 1 and 1+sin(cos^(-1)x)+sin^2(cos^(-1)x)+sin^3(cos^...

    Text Solution

    |

  8. The least value of (1+sec^(-1)x)(1+c a s^(-1)x) is

    Text Solution

    |

  9. Find the value of cot^(-1)3/4+sin^(-1)5/(13)

    Text Solution

    |

  10. If (x -1) (x^(2) + 1) gt 0, then find the value of sin((1)/(2) tan^(-1...

    Text Solution

    |

  11. Solve the following in equality sin^(-1)xlt=cos^(-1)xdot

    Text Solution

    |

  12. Solve sin^(-1)x+sin^(-1)2x=pi/3dot

    Text Solution

    |

  13. If a(1), a(2), a(3), …..a(n) is an arithmetic progression with common ...

    Text Solution

    |

  14. If x > y > z >0, then find the value of cot^(-1)(x y+1)/(x-y)+cot^(-1)...

    Text Solution

    |

  15. Find the value of 4tan^(-1)1/5-tan^(-1)1/(70)+tan^(-1)1/(99)

    Text Solution

    |

  16. Find the value of underset(r = 0) overset(oo)sum tan^(-1) ((1)/(1 + r ...

    Text Solution

    |

  17. If x in (0,pi/2), then show that cos^(-1)(7/2(1+cos2x)+sqrt((sin^2x-48...

    Text Solution

    |

  18. cos^(-1){1/2x^(2)+sqrt(1+x^(2))sqrt(1-x^(2))/(4)}=cos^(-1)(x)/(2)-cos^...

    Text Solution

    |

  19. Find the range of f(x)=|3tan^(-1)x-cos^(-1)(0)|-cos^(-1)(-1)dot

    Text Solution

    |

  20. Find the value of (i)sin^(-1)(2^x) (ii) cos^(-1)sqrt(x^2-x+1) (i...

    Text Solution

    |