Home
Class 12
MATHS
In any DeltaABC, prove that Sigma (sqr...

In any `DeltaABC`, prove that
`Sigma (sqrt(sinA))/(sqrt(sinB)+sqrt(sinC)-sqrt(sinA)) ge 3`
and the equality holds if and only if triangle is equilateral.

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos
  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|22 Videos
  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos
  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|9 Videos

Similar Questions

Explore conceptually related problems

In any DeltaABC , then minimum value of 2020sum (sqrt((sinA)))/((sqrt((sinB))+sqrt((sinC))-sqrt((sinA)))) must be

Prove that (sqrt5)/(3sqrt3) is irrational.

Prove that sqrt((1+sinA)/(1-sinA))=(1+sinA)/cosA .

Prove that (2sqrt7)/(sqrt11) is irrational.

What is ((sqrt3+i))/((1+sqrt3 i)) equal to ?

Prove that 4 sin 27^@ = sqrt(5+sqrt5)+sqrt(3-sqrt5) .

Prove that : cot frac (pi)(24)= sqrt2+ sqrt3+ sqrt4+ sqrt6 .

Prove that 5-sqrt3 is irrational.

Prove that 5-sqrt3 is irrational.

Prove that 2-sqrt3 is irrational.

ARIHANT MATHS-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (Subjective Type Questions)
  1. If alpha, beta, gamma are the roots of the cubic x^(3)-px^(2)+qx-r=0 ...

    Text Solution

    |

  2. The set of values of a for which the equation Sin^4 x + Cos^4 x = a ha...

    Text Solution

    |

  3. If aa n db are positive quantities such that a > b , the minimum value...

    Text Solution

    |

  4. If alpha+beta+gamma=2pi, then show that tan.alpha/2 + tan.beta/2 + tan...

    Text Solution

    |

  5. Eliminate theta from the equations tan(n theta+alpha)-tan(n theta+b...

    Text Solution

    |

  6. Let f(x)=cos(a1+x)+1/2cos(a2+x)+1/(2^2)cos(a1+x)++1/(2^(n-1))cos(an+x)...

    Text Solution

    |

  7. Eliminate theta from the equations tan(n theta+alpha)-tan(n theta+b...

    Text Solution

    |

  8. lf cos^2 alpha -sin^2 alpha = tan^2 beta, then show that tan^2 alpha...

    Text Solution

    |

  9. If A, B, C are the angle of a triangle and |(sinA,sinB,sinC),(cosA,...

    Text Solution

    |

  10. In any DeltaABC, prove that Sigma (sqrt(sinA))/(sqrt(sinB)+sqrt(sinC...

    Text Solution

    |

  11. Find all value of theta which satisfy, sin ( 3 theta + alpha ) + si...

    Text Solution

    |

  12. If the quadratic equation , 4^(sec^(2)alpha) x^(2) + 2x + (beta^(2)-...

    Text Solution

    |

  13. If 2costheta=x+1/x, prove that 2cos3theta=x^3+1/x^3

    Text Solution

    |

  14. If (cos theta(1))/(cos theta(2))+(sin theta(1))/(sin theta(2))=(cos th...

    Text Solution

    |

  15. Prove that sum(k=1)^(n-1) ""^(n)C(k)[cos k x. cos (n+k)x+sin(n-k)x.s...

    Text Solution

    |

  16. Solve sin 2x gt sqrt(2) sin^(2) x+ (2-sqrt(2))cos^(2)x

    Text Solution

    |

  17. The number of solutions of the equation cos[x]=e^(2x-1), x in [0, 2pi]...

    Text Solution

    |

  18. Prove that: sum(r=0)^(n) 3^( r) ""^(n)C(r) = 4^(n).

    Text Solution

    |

  19. Resolve Z^5+ 1 into linear & quadratic factors with real coefficients...

    Text Solution

    |

  20. Prove that the roots of the equation 8x^(3)-4x^(2)-4x+1=0 " are " co...

    Text Solution

    |