Home
Class 12
MATHS
If cos ^(-1)x + cos ^(-1) y + cos ^(-1) ...

If `cos ^(-1)x + cos ^(-1) y + cos ^(-1) z = pi,` then the value of `(xy sqrt (1 - z ^(2)) + yz sqrt (1 - x ^(2)) zx sqrt (1- y ^(2)))/( sqrt ((1- x^(2)) (1 - y ^(2)) ( 1 - z ^(2))))` is equal to

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • NTA TPC JEE MAIN TEST 51

    NTA MOCK TESTS|Exercise MATHEMATICS |30 Videos

  • NTA TPC JEE MAIN TEST 53

    NTA MOCK TESTS|Exercise MATHEMATICS|30 Videos

Similar Questions

Explore conceptually related problems

If sin ^ (- 1) x + sin ^ (- 1) y + sin ^ (- 1) z = pi, Prove x sqrt (1-x ^ (2)) + y sqrt (1-y ^ (2) ) + z sqrt (1-z ^ (2)) = 2xyz

If cos^(-1)x+cos^(-1)y+cos^(-1)z=3 pi, then xy+yz+zx is equal to

If sin^(-1) x + sin^(-1) y + sin^(-1) z = pi" , prove that " x sqrt(1-x^(2) ) + y sqrt(1 - y^(2)) + zsqrt( 1 - z^(2)) = 2 xyz .

If sin^(-1)x + sin^(-1)y + sin^(-1)z =pi , prove that xsqrt(1 - x^(2)) + y sqrt(1 -y^(2)) + z sqrt(1-z^(2))= 2xyz .

If cos^(-1) x + cos^(-1) y + cos^(-1) z = pi" , prove that " x^(2) + y^(2)+ z^(2) + 2xyz = 1 .

If cos^(-1)x + cos^(-1)y + cos^(-1)z = pi , then x^(2) + y^(2) + z^(2) + 2xyz is :

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

If sin^(-1)x +cos^(-1)y +sin^(-1)z=2pi then 2x-z+y is :

Prove that sin ^ (- 1) x + cos ^ (- 1) y = (tan ^ (- 1) (xy + sqrt ((1-x ^ (2)) (1-y ^ (2)))) ) / (y sqrt (1-x ^ (2)) - x sqrt (1-y ^ (2)))

If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi, where -1<=x,y,z<=1, then find the value of x^(2)+y^(2)+z^(2)+2xyz

NTA MOCK TESTS-NTA TPC JEE MAIN TEST 52-MATHEMATICS
  1. If a double ordinate of the parabola y ^(2) = 4 ax is of length 8a, th...

    Text Solution

    |

  2. If P,Q and R are three points with the co-ordinates (1,4),(4,2) and (m...

    Text Solution

    |

  3. The equation of the plane passing through the line of intersection of ...

    Text Solution

    |

  4. Let ABC be a triangle with vertices at points A (2,3,5), B (-1,3,) and...

    Text Solution

    |

  5. int (1)/(f (x)) dx = log (f (x)) ^(2) + C, then f (x) is

    Text Solution

    |

  6. If lim ( x to oo) ( sqrt ( x ^(2) + x +2 ) - ax -b )= 2, then equati...

    Text Solution

    |

  7. The sum of 50 observations and sum of their squares were found to be 2...

    Text Solution

    |

  8. int (dx)/( root (5) ( (x +1) ^((11)/(2)) (x +2) ^((9)/(2)))) is equal ...

    Text Solution

    |

  9. The contrapositive of the statement : If x = 5 and y =-2 then x - 2y ...

    Text Solution

    |

  10. If in Delta ABC, sin B cos C = (sqrt3 -1)/(sqrt3) and cos B sin C = (1...

    Text Solution

    |

  11. If cos ^(-1)x + cos ^(-1) y + cos ^(-1) z = pi, then the value of (xy ...

    Text Solution

    |

  12. If m be the number of direct common tangents to the circles x ^(2) + y...

    Text Solution

    |

  13. f (x) = {{:((sqrt2 + sin (1)/(x)) ^(( -1)/( e ^(|x|))), if x ne 0),(0,...

    Text Solution

    |

  14. Graphical representation of different functions is also a method of fi...

    Text Solution

    |

  15. Consider the differential equation (du)/(dt) = sin ( t + u ) + cos (t ...

    Text Solution

    |

  16. For a positive interger n, f (n) (x) = tan ((x)/(2)) (1 + sec x ) (1...

    Text Solution

    |

  17. Let f (x) = x ^(2) + {x} where {}represents fractional part. Given th...

    Text Solution

    |

  18. The curve y = ax ^(2) + bx + c passes through the point (1,2) and norm...

    Text Solution

    |

  19. Define a (k) = ( k ^(2) +1) k! and b (k) = a (1) + a (2) + a (3) + ......

    Text Solution

    |

  20. The first to two samples has 100 items with mean 15 and standard devia...

    Text Solution

    |