Home
Class 11
MATHS
The minimum value of the expression sin...

The minimum value of the expression `sin alpha + sin beta+ sin gamma`, where `alpha,beta,gamma` are real numbers satisfying `alpha+beta+gamma=pi` is
a. zero
b. -3
c. positive
d. negative

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

alpha, beta, gamma are real number satisfying alpha+beta+gamma=pi . The minimum value of the given expression sin alpha+sin beta+sin gamma is

If sin alpha+ sin beta+ sin gamma=3, then sin^3alpha+sin^3beta+sin^3 gamma=

the points (alpha,beta) , (gamma , delta) ,(alpha , delta) , (gamma , beta) are different real numbers are:

If tan beta=2sin alpha sin gamma co sec(alpha+gamma) , then cot alpha,cot beta,cotgamma are in

If 2 sin alphacos beta sin gamma=sinbeta sin(alpha+gamma),then tan alpha,tan beta and gamma are in

If alpha + beta + gamma = π/2 and cot alpha, cot beta, cot gamma are in Ap. Then cot alpha. Cot gamma

If cos alpha+cos beta+cos gamma=0=sin alpha+sin beta+sin gamma , then (sin3alpha+sin3beta+sin3gamma)/(sin(alpha+beta+gamma)) is equal to

If alphagt0, betagt0, gammagt0, alpha+beta+gamma= pi show that sin^2alpha+sin^2beta-sin^2gamma =

Determine the values of alpha ,beta , gamma when [{:( 0, 2beta, gamma),( alpha ,beta, -gamma),( alpha ,-beta, gamma):}] is orthogonal.

If p''(x) has real roots alpha,beta,gamma . Then , [alpha]+[beta]+[gamma] is

CENGAGE ENGLISH-TRIGONOMETRIC FUNCTIONS-All Questions
  1. A circle is inscribed in a triangle A B C touching the side A B at D s...

    Text Solution

    |

  2. In a triangle ABC, if sinAsin(B-C)=sinCsin(A-B), then prove that cotA...

    Text Solution

    |

  3. The minimum value of the expression sin alpha + sin beta+ sin gamma, ...

    Text Solution

    |

  4. In A B C ,cotA/2+cotB/2+cotC/2 is equal to Delta/(r^2) (b) ((a+b+...

    Text Solution

    |

  5. The value of theta in (0,2pi) for which 2sin^2theta-5sintheta+2>0 is (...

    Text Solution

    |

  6. In A B C , if cotA+cotB+cotC=0 then find the value of cosAcos BcosC

    Text Solution

    |

  7. Show that tan1^0tan2^0tan89^0=1

    Text Solution

    |

  8. In triangle ABC, the line joining the circumcenter and incenter is p...

    Text Solution

    |

  9. The number of solutions of the pair of equations 2sin^2 theta - cos(2 ...

    Text Solution

    |

  10. Given A=sin^2theta+cos^4theta, then for all real theta, (a)1lt=Alt...

    Text Solution

    |

  11. If A ,B ,C ,D are angles of a cyclic quadrilateral, then prove that c...

    Text Solution

    |

  12. The number of distinct real roots of |sinxcosxcosxcosxsinxcosxcosxcosx...

    Text Solution

    |

  13. D , E ,a n dF are the middle points of the sides of the triangle A B C...

    Text Solution

    |

  14. If cos(A-B)=3/5 and tan A tan B=2, then (a) cos Acos B=1/5 (b) sin A ...

    Text Solution

    |

  15. The number of ordered pairs (α,β), where α,β∈(−π,π) satisfying cos (α−...

    Text Solution

    |

  16. The base B C of A B C is fixed and the vertex A moves, satisfying the...

    Text Solution

    |

  17. For 0 < varphigeqpi/2,ifx=sum(n=0)^oocos^(2n)varphi,y=sum(n=0)^oosin^...

    Text Solution

    |

  18. In a right angled triangle, acute angle A and B satisfy tanA+tanB+tan^...

    Text Solution

    |

  19. Solve sin^2x+cos^2y=2sec^2z for x , y ,a n dzdot

    Text Solution

    |

  20. if 0ltalphaltbetaltgammaltpi/ 2,then prove that tanalpha lt (sinalpha+...

    Text Solution

    |