Home
Class 12
MATHS
If 0 lt x(1) lt x(2) lt x(3) lt pi then ...

If `0 lt x_(1) lt x_(2) lt x_(3) lt pi` then prove that sin `((x_(1) + x_(2) + x_(3))/(3)) gt (sin x_(1) + sin x_(2) + sin x_(3))/(3)` . Hence or otherwise prove that if A, B, C are angles of triangle then maximum value of sinA + sin B + sin C is `(3sqrt3)/(2)`

Promotional Banner

Topper's Solved these Questions

  • MAXIMA AND MINIMA

    MOTION|Exercise EXERCISE -1 (SECTION - A)|7 Videos

  • MAXIMA AND MINIMA

    MOTION|Exercise EXERCISE -1 (SECTION -B)|16 Videos

  • MATRICES

    MOTION|Exercise Exercise - 4 (Level-II)|28 Videos

  • METHOD OF DIFFERENTIATION

    MOTION|Exercise EXERCISE - 4 LEVEL -II|5 Videos

Similar Questions

Explore conceptually related problems

If

Prove that ((sin ^ (3) x) / (1 + cos x) + (cos ^ (3) x) / (1-sin x)) = sqrt (2) sin ((pi) / (4) + x)

If x lt 0 , then prove that cos^(-1) x = pi - sin^(-1) sqrt(1 - x^(2))

If 0 lt x lt pi/2 then the largest angle of a triangle whose sides are 1, sin x, cos x is

[ If 0ltxlt(pi)/(2) then 1) (2)/(pi)gt(sin x)/(x) (2) (pi)lt(sin x)/(x) 3) (sin x)/(x)gt1 , 4) 2lt(sin x)/(x)

If 0 lt x lt (pi)/(2) , then ("sin x + cosec x") is

For x in (0,(pi)/(2)) prove that "sin"^(2) x lt x^(2) lt " tan"^(2) x

If "sin"A=(1)/(2)(x+(1)/(x)) ,prove that: "sin" 3A+(1)/(2)(x^(3)+(1)/(x^(3)))=0 .

Prove that sin^(-1). ((x + sqrt(1 - x^(2))/(sqrt2)) = sin^(-1) x + (pi)/(4) , where - (1)/(sqrt2) lt x lt(1)/(sqrt2)

MOTION-MAXIMA AND MINIMA -EXERCISE - 4 (LEVEL - II)
  1. If 0 lt x(1) lt x(2) lt x(3) lt pi then prove that sin ((x(1) + x(2) +...

    Text Solution

    |

  2. The total number of local maxima and local minima of the function f(x)...

    Text Solution

    |

  3. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  4. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  5. Consider the function f : (-oo , oo) to (-oo , oo) defined by f(x) = (...

    Text Solution

    |

  6. Let p(x) be a polynomial of degree 4 having extremum at x = 1, 2 and u...

    Text Solution

    |

  7. The maximum value of the function f(x)=2x^(3)-15x^(2)+36x-48 on the se...

    Text Solution

    |

  8. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  9. Let f be a function defined on R (the set of all real numbers) such th...

    Text Solution

    |

  10. The number of distinct real roots of x^(4)-4x^(3)+12x^(2)+x-1=0

    Text Solution

    |

  11. Let p(x) be a real polynomial of least degree which has a local maximu...

    Text Solution

    |

  12. Let I RvecI R be defined as f(x)=|x|++x^2-1|dot The total number of po...

    Text Solution

    |

  13. If f(x) = underset(0)overset(x)inte^(t^(2)) (t-2) (t-3) dt for all x ...

    Text Solution

    |

  14. A rectangular sheet of fixed perimeter with sides having their lengths...

    Text Solution

    |

  15. The function f(x)=2|x|+|x+2|-||x+2|-2|x|| has a local minimum or a lo...

    Text Solution

    |

  16. Let f:RtoR and g:RtoR be respectively given by f(x)=|x|+1 and g(x)=x^(...

    Text Solution

    |

  17. A cylindrical container is to be made from certain solid material with...

    Text Solution

    |

  18. The least value of alpha in R for which 4alphax^(2)+(1)/(x)ge1, for al...

    Text Solution

    |