Home
Class 12
MATHS
If cos^-1x + cos^-1y+cos^-1z = pi then s...

If `cos^-1x + cos^-1y+cos^-1z = pi` then show that `x^2+y^2+z^2+2xyz = 1`

Promotional Banner

Topper's Solved these Questions

  • Trignometric Functions

    CHETANA PUBLICATION|Exercise EXERCISE|113 Videos

  • PROBABILITY DISTRIBUTIONS

    CHETANA PUBLICATION|Exercise EXERCISE|108 Videos

Similar Questions

Explore conceptually related problems

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

If tan^-1x+tan^-1y+tan^-1z = frac{pi}{2} , then show that xy+xy+zx = 1

If y= cos(m cos^(-1) x), then show that (1- x^2 ) ( d^2 y)/(d x^2 ) - x(dy/dx) + m^2 y =0

If cot^(-1)x+cot^(-1)y+cot^(-1)z=(pi)/(2) , then x+y+z=

If sinx+sin^2x=1 then show that cos^2 x +cos^4 x=1

If y= sin(m cos^(-1) x), then show that (1- x^2 )( d^2 y)/(d x^2 ) - x dy/dx + m^2 y =0

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

If x= cos theta , y= sin^3 theta , show that y ( d^2 y)/(d x^2 ) + (dy/dx)^2 = 3 sin^2 theta (5 cos^2 theta - 1)

If x= cos theta , y= sin^3 theta , show that y( d^2 y)/(d x^2 ) + (dy/dx)^2 = 3 sin^2 theta (5 cos^2 theta - 1)

If y= A cos(log x) + B sin(log x) , show that x^2 y_2 + xy_1 + y =0

CHETANA PUBLICATION-Trignometric Functions-EXERCISE
  1. If cos^-1x + cos^-1y+cos^-1z = pi then show that x^2+y^2+z^2+2xyz = 1

    Text Solution

    |

  2. Find the general solutions of the following equations: sintheta = frac...

    Text Solution

    |

  3. Find the general solutions of the following equations: costheta = frac...

    Text Solution

    |

  4. Find the general solutions of the following equations: tantheta = sqrt...

    Text Solution

    |

  5. Find the general solutions of the following equations: sintheta = -fra...

    Text Solution

    |

  6. Find the general solutions of the following equations: costheta = -fra...

    Text Solution

    |

  7. Find the general solutions of the following equations: cottheta = -sqr...

    Text Solution

    |

  8. Find the general solutions of the following equations: 4cos^2theta = 1

    Text Solution

    |

  9. Find the general solutions of the following equations: 4sin^2theta = 3

    Text Solution

    |

  10. Find the general solutions of the following equations: tan^2theta = 1

    Text Solution

    |

  11. Find the general solutions of the following equations: cos3theta = cos...

    Text Solution

    |

  12. Find the general solutions of the following equations: cos5theta = sin...

    Text Solution

    |

  13. Find the general solutions of the following equations: sec^2(2theta) =...

    Text Solution

    |

  14. Find the general solutions of the following equations: 4sinxcosx+2sinx...

    Text Solution

    |

  15. Find the general solutions of the following equations: sin2x+sin4x+sin...

    Text Solution

    |

  16. Find general solution of sqrt3cosx-sinx = 1

    Text Solution

    |

  17. Solve the triangle in which a=2,b=1 and c=sqrt3

    Text Solution

    |

  18. In any /\ABC, prove that asinA-bsinB = csin(A-B)

    Text Solution

    |

  19. In any /\ABC, prove that [frac{a-b}{a+b}] = frac{tan(frac{A-B}{2})}{ta...

    Text Solution

    |

  20. In any /\ABC, prove that frac{a^2sin(B-C)}{sinA}+frac{b^2sin(C-A)}{sin...

    Text Solution

    |

  21. For /\ABC, prove that frac{cosA}{c cosB+bcosC}+frac{cosB}{acosC+c cosA...

    Text Solution

    |