Home
Class 12
MATHS
if cos^(-1)x+cos ^(-1)y+cos^(-1) z=pi ...

if ` cos^(-1)x+cos ^(-1)y+cos^(-1) z=pi` prove that
` x^(2) +y^(2)+z^(2) +2xyz=1`

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC INVERSE CIRCULAR FUNCTIONS

    CHHAYA PUBLICATION|Exercise Long answer type questions|28 Videos

  • TRIGONOMETRIC INVERSE CIRCULAR FUNCTIONS

    CHHAYA PUBLICATION|Exercise sample questions for competive examination|20 Videos

  • TRIGONOMETRIC INVERSE CIRCULAR FUNCTIONS

    CHHAYA PUBLICATION|Exercise Very short answer type Questions|39 Videos

  • TRANSFORMATIONS OF SUMS AND PRODUCTS

    CHHAYA PUBLICATION|Exercise Comprehension Type|6 Videos

  • TRIGONOMETRIC RATIOS OF ASSOCIATED ANGLES

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTIONS FOR COMPETITIVE EXAMS - ASSERTION-REASON TYPE|2 Videos

Similar Questions

Explore conceptually related problems

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

if tan ^(-1) x+tan ^(-1) y+tan ^(-1) z=pi prove that x+y+z=xyz

"if " sin^(-1) x +sin ^(-1) y+sin ^(-1) z=pi show 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))

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

If cos^(-1)x + cos^(-1)y + cos^(-1)z = 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))+ysqrt(1-y^(2))+zsqrt( 1-z^(2))= 2 xyz.

if cos ^(-1 ) ""(x )/(a) + cos ^(-1 )""(y)/(b ) = alpha prove that , (x^(2) )/(a^(2)) -(2xy)/(ab ) ""cos alpha +(y^(2))/(b^(2))= sin ^(2) alpha

Let x , y , z be non - zero real numbers lying in the interval [-1,1] such that cos^-1 x + cos^-1 y + cos^-1 z = pi The value of x^2 + y^2 + z^2 is equal to

If sin^-1x + 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^2)

If cos^(-1).(x)/(2) + cos^(-1).(y)/(3) = (pi)/(6) , then prove that (x^(2))/(4) - (xy)/(2sqrt3) + (y^(2))/(9) = (1)/(4)

CHHAYA PUBLICATION-TRIGONOMETRIC INVERSE CIRCULAR FUNCTIONS-Short answer type questions
  1. cos (2cos ^(-1) x+sin ^(-1) x) , " when " x=(1)/(5) where 0 le ...

    Text Solution

    |

  2. 2 tan ^(-1)""(1+x)/(1-x)+sin ^(-1)""(1-x^(2))/(1+x^(2))

    Text Solution

    |

  3. tan (sin ^(-1)x+sin ^(-1) y) +tan (cos^(-1)x+cos ^(-1)y)

    Text Solution

    |

  4. If xy=1 + a^(2) then show that tan^(-1) ""(1)/(a+x)+tan ^(-1) ...

    Text Solution

    |

  5. "If " tan^(-1) x+ tan^(-1) y+tan ^(-1)z=(pi)/(2) , show that , x...

    Text Solution

    |

  6. if tan ^(-1) x+tan ^(-1) y+tan ^(-1) z=pi prove that x+y+z=xyz

    Text Solution

    |

  7. if cos^(-1)x+cos ^(-1)y+cos^(-1) z=pi prove that x^(2) +y^(2)+z...

    Text Solution

    |

  8. "if " sin^(-1) x +sin ^(-1) y+sin ^(-1) z=pi show that , x^(4)+y...

    Text Solution

    |

  9. IF cos (alpha +beta )=(5)/(13) and cos (alpha - beta )=(4)/(5), t...

    Text Solution

    |

  10. If tan ^(-1) y= 4 tan ^(-1) x , find the algebric relation bet...

    Text Solution

    |

  11. If tan ^(-1)x , tan ^(-1) y and tan^(-1) z are in A.P find t...

    Text Solution

    |

  12. tan ^(-1) (x+1) + tan^(-1) (x-1) = tan ^(-1)"" (8)/(31)

    Text Solution

    |

  13. tan (cos ^(-1) x) = sin (cot ^(-1) ""(1)/(2))

    Text Solution

    |

  14. tan ^(-1)((1)/(2) sec x) + cot^(-1)(2cos x) =(pi)/(3)

    Text Solution

    |

  15. sin ^(-1) ""(2a)/(1+a^(2))+sin ^(-1) ""(2b)/(1+b^(2) ) = 2 tan ^(-1...

    Text Solution

    |

  16. tan ^(-1) ""(x-1)/(x-2) + tan ^(-1) ""(x+1)/(x+2)=(pi)/(4)

    Text Solution

    |

  17. tan ^(-1) ""(x-1)/(x-2) +tan ^(-1) ""(x+1)/(x+2)=(pi)/(4)

    Text Solution

    |

  18. sin ^(-1)cos sin^(-1)""x=(pi)/(3)

    Text Solution

    |

  19. tan^(-1)x+tan^(-1) (1-x) = 2 tan ^(-1) sqrt(x(1-x))

    Text Solution

    |

  20. 3 sin ^(-1 ) ""(2x )/(1+x^(2))-4cos^(-1) ""(1-x^(2))/(1+x^(2))+2tan ^...

    Text Solution

    |