Home
Class 12
MATHS
In a !ABC if sin A cos B = 1/4 and 3 tan...

In a `!ABC` if sin A cos B = `1/4` and 3 tan A = B , then the triangle is

A

right angled at A

B

right angled at B

C

right angled at C

D

not right angled

Text Solution

Verified by Experts

We have,
`3tanA=tanB`
`rArr3sinAcosB-=sinBcosA`
`rArr3/4=sinBcosA [becausesinAcosB=1/4]`
Thus, we have
`sinAcosB=1/2` and `sinBcosA=3/4`
`rArrsinAcosB+sinBcosA=1/4+3/4`
`rArrsin(A+B)=1rArra+B=(pi)/2rArrC=pi/2`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA|Exercise SOLVED MCQ|2 Videos

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|13 Videos

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA|Exercise Chapter Test|55 Videos

  • PLANE AND STRAIGHT LINE IN SPACE

    OBJECTIVE RD SHARMA|Exercise Chapter Test|31 Videos

  • REAL FUNCTIONS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|60 Videos

Similar Questions

Explore conceptually related problems

In triangle ABC, if sin A cos B=(1)/(4) and 3tan A=tan B, then cot ^(2)A is equal to (a)2 (b) 3 (c) 4 (d) 5 .

If in a Delta ABC, cos B = (sin A)/(2 sin C), then the triangle is

In Delta ABC, if sin^(4)A sin B sin C=1-cos B cos C then triangle is necessarily

In Delta ABC, If tan B tan C+tan C tan A+tan A tan B=sqrt(3)tan A tan B tan C then the triangle is

If sinA=sin^2B and 2cos^2A=3cos^2B then the triangle ABC is

OBJECTIVE RD SHARMA-PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM-Section I - Solved Mcqs
  1. If a chord AB of a circle subtends an angle theta(nepi//3) at a point ...

    Text Solution

    |

  2. In a !ABC , medians AD and BE are drawn. If AD = 4, angleDAB=pi//6 and...

    Text Solution

    |

  3. In a !ABC if sin A cos B = 1/4 and 3 tan A = B , then the triangle is

    Text Solution

    |

  4. In a !ABC if r(1) = 36 , r(2) = 18 and r(3) = 12, then the area of the...

    Text Solution

    |

  5. In a !ABC if r(1) = 36 , r(2) = 18 and r(3) = 12 , then the perimeter ...

    Text Solution

    |

  6. If in a Delta ABC, AD, BE and CF are the altitudes and R is the circum...

    Text Solution

    |

  7. In a !ABC if a = 7 , b = 8 and c = 9 , then the length of the line joi...

    Text Solution

    |

  8. If the perimeter of a triangle and the diameter of an ex-circle are eq...

    Text Solution

    |

  9. If D id the mid-point of the side BC of a triangle ABC and AD is perpe...

    Text Solution

    |

  10. ABC is a triangle. D is the middle point of BC. If AD is perpendicular...

    Text Solution

    |

  11. If the median of a triangle through A is perpendicular to AB, then

    Text Solution

    |

  12. In a !ABC , if r(1) =2r(2) =3r(3) , then a:b:c =

    Text Solution

    |

  13. In a !ABC if r(1)ltr(2)ltr(3), then

    Text Solution

    |

  14. In a !ABC if r(1) = 8, r(2) = 12 and r(3) = 24, then a =

    Text Solution

    |

  15. If I is the incentre of a DeltaABC such that angleA=60^(@), then AI =

    Text Solution

    |

  16. If I(1) is the centre of the escribed circle touching side BC of Delta...

    Text Solution

    |

  17. In a !ABC , if 2R + r = r(1) , then

    Text Solution

    |

  18. The sides of the triangle are sinalpha , cosalpha and sqrt(1+sinalphac...

    Text Solution

    |

  19. In a !ABC , if 3a = b + c , then cot B/2 cot C/2 =

    Text Solution

    |

  20. In !ABC , if sin^(2)A/2,sin^(2)B/2,sin^(2)C/2 be in H.P., then a , b ,...

    Text Solution

    |