Home
Class 12
MATHS
Consider the following statements concer...

Consider the following statements concerning a `DeltaABC`
(i) The sides a,b,c and area of triangle are rational.
(ii) `a, "tan"(B)/(2),"tan"(C)/(2)`
(iii) `a, sin A sin B, sin C` are rational .
Prove that `(i) rArr(ii) rArr(iii)rArr(i)`

Text Solution

Verified by Experts

The correct Answer is:
Hence `(iii)=>(i).`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise SOLVED EXAMPLES|1 Videos
  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise For Sesssion 1|20 Videos
  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|52 Videos
  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

Similar Questions

Explore conceptually related problems

If in DeltaABC, A =90^(@) and c, sin B and cos B are rational number, then

In any DeltaABC, find sin A+sin B+ sin C.

In DeltaABC, if sin^2 A+ sin^2 B = sin^2 C , then the triangle is

If the sides a,b,c are in A.P., prove that (tan)A/2+ (tan) c/2=2/3( cot) B/2.

If a,b,c are in HP, then prove that sin ^(2) ""(A)/(2), sin ^(2) ""(B)/(2), sin ^(2) ""(C )/(2) are also in HP.

In any triangle ABC, if sin A , sin B, sin C are in AP, then the maximum value of tan ""B/2 is

In any triangle ABC, prove that : (sin(B-C))/(sin(B+C))= (b^2 -c^2)/a^2 .

In any triangle ABC, prove that : sin (A + B) = sin C .

In any triangle ABC, prove that : sin frac (A-B)(2)= (a-b)/c cos frac (C)(2) .

In any triangle ABC, prove that : (a-b)/c= (sin frac (A-B)(2))/(cos frac (C)(2)) .

ARIHANT MATHS-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Consider the following statements concerning a DeltaABC (i) The sid...

    Text Solution

    |

  2. Prove that 2sin^2(pi/6) - sec^2(pi/3)= -7/2

    Text Solution

    |

  3. In a triangle the sum of two sides is x and the product of the same is...

    Text Solution

    |

  4. Consider a triangle A B C and let a , b and c denote the lengths of th...

    Text Solution

    |

  5. Solution of differential equation 2xy dy / dx = x^2 + 3y^2 is .

    Text Solution

    |

  6. Let PQR be a triangle of area Delta with a = 2, b = 7//2, and c = 5//2...

    Text Solution

    |

  7. If the angle A ,Ba n dC of a triangle are in an arithmetic propression...

    Text Solution

    |

  8. Let A B C be a triangle such that /A C B=pi/6 and let a , b and c deno...

    Text Solution

    |

  9. A triangle A B C with fixed base B C , the vertex A moves such that co...

    Text Solution

    |

  10. Let A B Ca n dA B C ' be two non-congruent triangles with sides A B=4,...

    Text Solution

    |

  11. A straight line through the vertex P of a triangle P Q R intersects th...

    Text Solution

    |

  12. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  13. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  14. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  15. Internal bisector of /A of triangle ABC meets side BC at D. A line dra...

    Text Solution

    |

  16. One angle of an isosceles triangle is 120^0 and the radius of its incr...

    Text Solution

    |

  17. In Delta ABC, which one is true among the following ?

    Text Solution

    |

  18. Let a vertical tower A B have its end A on the level ground. Let C be ...

    Text Solution

    |

  19. ABCD is a trapezium such that AB and CD are parallel and BC bot CD. If...

    Text Solution

    |

  20. For a regular polygon, let r and R be the radii of the inscribed and t...

    Text Solution

    |

  21. In triangle A B C , let /c=pi/2dot If r is the inradius and R is circu...

    Text Solution

    |