Home
Class 11
MATHS
If Sin^(-1)(x)+Sin^(-1)(y)+Sin^(-1)(z) =...

If `Sin^(-1)(x)+Sin^(-1)(y)+Sin^(-1)(z) = pi`, prove that `xsqrt(1-x^(2)) + ysqrt(1-y^(2)) +zsqrt(1-z^(2)) = 2xyz`.

Text Solution

Verified by Experts

The correct Answer is:
`2 xyz`.
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise SOLVED PROBLEMS|32 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISES ( EXERCISE - 8(a) II).|17 Videos

  • HYPERBOLIC FUNCTIONS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE - 9(a)|10 Videos

  • LIMITS AND CONTINUITY

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise Exercise 8(e)|12 Videos

Similar Questions

Explore conceptually related problems

If Sin^(-1)x+Sin^(-1)y+Sin^(-1)z=pi then prove that n xsqrt(1-x^(2))+ysqrt(1-y^(2))+zsqrt(1-z^(2))=2xy z

Sin^(-1)(xsqrt(1-y^(2))+ysqrt(1-x^(2)))=

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^(2)x^(2)) .

Solve Sin^(-1)x +Sin^(-1)2x = (pi)/3 .

If Tan^(-1) x + Tan^(-1) y + Tan^(-1) z = pi then prove that x+y+z = xyz .

If sin^(-1)(x)+sin^(-1)(2x)=(pi)/3 then x=

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-INVERSE TRIGONOMETRIC FUNCTIONS-TEXTUAL EXERCISES ( EXERCISE - 8(a) III).
  1. కింది వాటిని రుజువు చేయండి. 4 tan^-1 (1/5) + tan^-1 (1/99) - tan^-1 (1...

    Text Solution

    |

  2. If alpha = Tan^(-1)((sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2)...

    Text Solution

    |

  3. tan[2Tan^(-1)((sqrt(1+x^(2))-1)/x)]=

    Text Solution

    |

  4. Prove that sin[Cot^(-1) (2x)/(1-x^2)+Cos^(-1)((1-x^(2))/(1+x^(2)))]=1.

    Text Solution

    |

  5. Prove that tan{(pi)/4 + 1/2 Cos^(-1)((a)/(b))}+tan{((pi)/4-1/2 Cos^(-1...

    Text Solution

    |

  6. If Cos^(-1)p+Cos^(-1)q+Cos^(-1)r = pi then, P.T. p^(2)+q^(2)+r^(2) = 2...

    Text Solution

    |

  7. If Sin^(-1)(2p)/(1+p^(2)) - Cos^(-1)((1-q^(2))/(1+q^(2))) = Tan^(-1) (...

    Text Solution

    |

  8. Id a,b,c are distinct non-zero real numbers having the same sign. Prov...

    Text Solution

    |

  9. If Sin^(-1)(x)+Sin^(-1)(y)+Sin^(-1)(z) = pi, prove that xsqrt(1-x^(2))...

    Text Solution

    |

  10. If Tan^(-1) x + Tan^(-1) y + Tan^(-1) z = pi then prove that x+y+z = x...

    Text Solution

    |

  11. If Tan^(-1)x+Tan^(-1)y + Tan^(-1)z = (pi)/2, then prove that xy + yz +...

    Text Solution

    |

  12. If tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/(x+2))=(pi)/4 then x=

    Text Solution

    |

  13. The arithmetic mean of the non-zero solutions of the equation "Tan"^...

    Text Solution

    |

  14. Solve 3Sin^(-1)((2x)/(1+x^(2))) - 4 Cos^(-1)((1-x^(2))/(1+x^(2)))+2Tan...

    Text Solution

    |

  15. Solve the following equations : sin^(-1)(1-x)-2sin^(-1)x=(pi)/2 the...

    Text Solution

    |

  16. solve the following equations Cot^(-1)((1+x)/(1-x))=1/2Cot^(-1)(1/x)...

    Text Solution

    |

  17. Solve the following equations. (ii) tan [ chi o sigma^(-1) (1)/( xi)...

    Text Solution

    |

  18. Solve the following equations. cos^(-1) x + sin^(-1) "" (x)/(2) = (...

    Text Solution

    |

  19. solve the following equations Cos^(-1) (sqrt(3).x)+Cos^(-1)(x)=(pi)/...

    Text Solution

    |

  20. Solve the following equations. sin [ sin^(-1) ((1)/(5)) + cos^(-1) x...

    Text Solution

    |