Home
Class 12
MATHS
Let cosA+cosB + cos C=3/2 in a triangle ...

Let `cosA+cosB + cos C=3/2` in a triangle then the type of the triangle is

Text Solution

Verified by Experts

The correct Answer is:
Similarly, we can show B = C, C = A. Hence, the triangle is equilateral.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Solved Examples : Single Option Correct Type Questions|2 Videos
  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise For Session 1|10 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

If in a triangle A B C ,cosA+2cosB+cosC=2 prove that the sides of the triangle are in AP

If p_1, p_2, p_3 are the altitudes of a triangle from the vertices A, B, C and triangle , the area of the triangle, prove that : 1/p_1+1/p_2-1/p_3= (2ab)/((a+b+c)triangle) cos^2 frac (C)(2) .

Do the points (3, 2), (-2, -3) and (2, 3) form a triangle? If so, name the type of triangle formed.

Let A(h, k), B(1, 1) and C(2, 1) be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1, then the set of values which k can take is given by (1) {1,""3} (2) {0,""2} (3) {-1,""3} (4) {-3,-2}

Let the complex numbers z_1,z_2,z_3 be the vertices of an equilateral triangle. Let z_0 be the circumcentre of the triangle. Then prove that z_1^2+z_2^2+z_3^2= 3z_0^2 .

Let PQR be a triangle of area Delta with a = 2, b = 7//2 , and c = 5//2 , where a, b and c are the lengths of the sides of the triangle opposite to the angles at P, Q and R, respectively. Then (2 sin P - sin 2P)/(2 sin P + sin 2P) equals

If in a triangle a cos^(2).(C)/(2) + c cos^(2).(A)/(2) = (3b)/(2) , then find the relation between the sides of the triangles

If in a triangle, a/(cosA)= b/(cos B) =c/(cos C) , then the triangle is :

In any DeltaABC, is 2 cos B=a/c, then the triangle is

In a triangle ABC, cos 3A + cos 3B + cos 3C = 1 , then find any one angle.

ARIHANT MATHS-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let cosA+cosB + cos C=3/2 in a triangle then the type of the triangle ...

    Text Solution

    |

  2. Let alpha and beta be non-zero real numbers such that 2 ( cos beta -...

    Text Solution

    |

  3. Let -pi/6 < theta < -pi/12. Suppose alpha1 and beta1, are the roots of...

    Text Solution

    |

  4. The value of overset(13)underset(k=1)(sum) (1)/(sin((pi)/(4) + ((k-1)p...

    Text Solution

    |

  5. Let f:(-1,1)vecR be such that f(cos4theta)=2/(2-sec^2theta) for theta ...

    Text Solution

    |

  6. The number of all possible values of theta, where 0 lt theta lt pi, fo...

    Text Solution

    |

  7. For 0 lt theta lt pi/2 , the solution (s) of sum(m=1)^6cos e c(theta+(...

    Text Solution

    |

  8. If sin^ 4 x/2+cos^4 x/3 =1/5 then

    Text Solution

    |

  9. Let theta in (0, pi/4) and t(1)=tan theta)^(tan theta), t(2)=(tan thet...

    Text Solution

    |

  10. if cos(alpha-beta)=1a n dcos(alpha+beta)=l/e , where alpha,betamu in [...

    Text Solution

    |

  11. If 5 (tan ^(2) x - cos ^(2) x ) = 2 cos 2x +9, then the value of cos 4...

    Text Solution

    |

  12. Let F(k)(x)=1/k (sin^(k)x+cos^(k)x), where x in R and k ge 1, then fin...

    Text Solution

    |

  13. The expression (tanA)/(1-cotA)+(cotA)/(1-tanA) can be written as (1) s...

    Text Solution

    |

  14. If a Delta PQR " if" 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P =1 , ...

    Text Solution

    |

  15. If A = sin^2x + cos^4 x, then for all real x :

    Text Solution

    |

  16. Let cos(alpha+beta)""=4/5 and let sin (alpha+beta)""=5/(13) where 0lt=...

    Text Solution

    |

  17. If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma, then which...

    Text Solution

    |

  18. A triangular park is enclosed on two sides by a fence and on the third...

    Text Solution

    |

  19. In Delta PQR , /R=pi/4, tan(P/3), tan(Q/3) are the roots of the equati...

    Text Solution

    |