Home
Class 10
MATHS
If x=rsinAcosC ,\ \ y=rsinAsinC and z=rc...

If `x=rsinAcosC ,\ \ y=rsinAsinC` and `z=rcosA` , prove that `r^2=x^2+y^2+z^2`

Promotional Banner

Topper's Solved these Questions

  • 2020 QUESTION PAPER (1)

    AGRAWAL PUBLICATION|Exercise EXERCISE|33 Videos

Similar Questions

Explore conceptually related problems

If x=r sin A cos C,quad y=r sin A sin C and z=r cos A, prove that r^(2)=x^(2)+y^(2)+z^(2)

If x=r sin alpha cos beta, y= r sin alpha sin beta and z= r cos alpha , prove that x^(2)+y^(2) + z^(2) = r^(2).

If x=r sin theta cos varphi,y=r sin theta sin varphi and z=r cos theta, then x^(2)+y^(2)+z^(2)=r^(2)(b)x^(2)+y^(2)-z^(2)=r^(2)(c)x^(2)-y^(2)+z^(2)=r^(2)(d)z^(2)+y^(2)-x^(2)=r^(2)

If x=r cos A cos B, y=rcosAsinB, z=rsin A then x^(2)+y^(2)+z^(2)=

If sin^-1 x+sin^-1 y+sin^-1 z= pi prove that: x^4+y^4+z^4+4x^2y^2z^2=2(x^2y^2+y^2z^2+z^2x^20

If z = x + iy and |z+6| = |2z+3| , prove that x^2+y^2 =9.

Using properties of determinant prove that: |[1,x+y, x^2+y^2],[1, y+z, y^2+z^2],[1, z+x, z^2+x^2]|= (x-y)(y-z)(z-x)

a, b, x are in AP, a, b, y are in GP and a, b, z are in HP, then prove that 4z(x-y)(y-z)=y(x-z)^2 .

If x + y + z = xyz , prove that x(1 -y^(2)) (1- z^(2))+ y(1- z^(2))(1- x^(2)) +z(1-x^(2)) (1- y^(2)) = 4xyz .

Using properties of determinants, prove that |[2y,y-z-x,2y],[2z,2z, z-x-y],[ x-y-z, 2x,2x]|=(x+y+z)^3

AGRAWAL PUBLICATION-(2019) QUESTION PAPER-EXAMPLE
  1. If x=rsinAcosC ,\ \ y=rsinAsinC and z=rcosA , prove that r^2=x^2+y^...

    Text Solution

    |

  2. Check whether g(x) is a factor of P(x) by dividing polynomial p(x) by ...

    Text Solution

    |

  3. Find the area of the triangle formed by joining the mid-points of the ...

    Text Solution

    |

  4. Draw the graph of the equations x-y+ 1 = 0 and 3x + 2y - 12 = 0. Using...

    Text Solution

    |

  5. Prove that sqrt 3 is an irrational number.

    Text Solution

    |

  6. Find the greatest number which on dividing 1251, 9377 and 15628 leaves...

    Text Solution

    |

  7. A,B and C are interior angles of a triangle ABC. Show that sin[(B+C)/2...

    Text Solution

    |

  8. If angle A = 90^@, then find the value of tan [(B + C)/2]

    Text Solution

    |

  9. If tan(A +B) = 1 and tan(A - B) = 1/ sqrt 3, 0^@ < A + B < 90^@, A>B, ...

    Text Solution

    |

  10. In Figure, PQ is a chord of length 8 cm of a circle of radius 5 cm. Th...

    Text Solution

    |

  11. Prove that opposite sides of a quadrilateral circumscribing a circel s...

    Text Solution

    |

  12. Water in a canal, 6 m wide an 1.5 m deep, is flowing with a speed of 1...

    Text Solution

    |

  13. A class teacher has the following absentee record of 40 students of a ...

    Text Solution

    |

  14. A car has two wipers which do not overlap. Each wiper has a blade of l...

    Text Solution

    |

  15. A pole has to be erected at a point on the boundary of a circular park...

    Text Solution

    |

  16. If m times the m^(th) term of an Arithmetic Progession is equal to n t...

    Text Solution

    |

  17. The sum of the first three numbers is an Arithmetic Progression is 18....

    Text Solution

    |

  18. Construct a triangle ABC with side BC = 6 cm, AB = 5 cm and angle ABC ...

    Text Solution

    |

  19. In Figure, a decorative block is shown which is made of two solids, a ...

    Text Solution

    |

  20. In Figure, a decorative block is shown which is made of two solids, a ...

    Text Solution

    |

  21. A bucket open at the top is in the form of a frustum of a cone with a ...

    Text Solution

    |