Home
Class 12
MATHS
If A , B , C are angles in a triangle ,...

If `A , B , C ` are angles in a triangle , then prove that ` sin A + sin B + sin C =4 cos. (A)/(2) cos . (B)/(2) cos .(C)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
`=4 cos. (A)/(2) cos. (B)/(2) cos. (C)/(2)=R.H.S`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIONS, TRANSFORMATIONS

    SRISIRI PUBLICATION|Exercise VSAQ|51 Videos
  • TRIGONOMETRIC EQUATIONS

    SRISIRI PUBLICATION|Exercise SPQ|8 Videos

Similar Questions

Explore conceptually related problems

If A, B, C are angles in a triangle , prove that sin A+ sin B -sin C =4sin. (A)/(2)sin. (B)/(2) cos. (C)/(2)

If A, B , C are angles in a triangle, then prove that sin ^(2)A+ sin ^(2)B+sin^(2)C=2+2 cos A cos B cos C

If A,B, C are angles in a triangle, then prove that: sin^(2) A + sin^(2) B - sin^(2) C =2 sin A sin B cos C

If A, B, C are angles of a triangle , prove that sin 2A+sin 2B-sin 2C=4cos Acos B sin C

If A,B,C are angles in a triangle , then prove that cosA+cosB+cosC=1+4sin. (A)/(2)sin. (B)/(2) sin. (C)/(2)

If A, B, C are angles of a triangle , prove that cos 2A+cos 2B -cos 2C=1-4 sin A sin B cos C

If A, B, C are angles of a triangle, then S. T sin 2A -sin 2B + sin 2C=4 CosA sin B CosC

If A, B , C are angles in a triangle, then the sin ^(2)A+sin ^(2)B - sin ^(2) C =2 sin A sin B cos C

If A, B, C are angles of a triangle , prove that cos 2A - cos 2B + cos 2C =1 -4 sin A cos B sin C

If A, B, C are the angles of a triangle, prove that sin2A+sin2B+sin2C=4sinAsinBsinC

SRISIRI PUBLICATION-TRIGONOMETRIC RATIONS, TRANSFORMATIONS-LAQ
  1. If A, B, C are angles of a triangle, then S. T sin 2A -sin 2B + sin...

    Text Solution

    |

  2. If A, B, C are angles of a triangle , prove that cos 2A - cos 2B + ...

    Text Solution

    |

  3. If A , B , C are angles in a triangle , then prove that sin A + sin ...

    Text Solution

    |

  4. IF A,B,C are angles in the triangle, then prove that cosA+cosB-cosC=...

    Text Solution

    |

  5. If A, B , C are angles in a triangle, then the sin ^(2)A+sin ^(2)B - s...

    Text Solution

    |

  6. If A+B+ C =pi, then prove that cos ^(2) (A/2)+ cos ^(2) (B/2) +cos ^(2...

    Text Solution

    |

  7. If A, B , C are angles of a triangle, then P. T sin ^(2) . (A)/(2)+ si...

    Text Solution

    |

  8. In triangle ABC, prove that cos .(A)/(2)+cos.(B)/(2)+cos. (C)/(2) =4 c...

    Text Solution

    |

  9. If A, B, C are the angles in a triangle then prove that sin .(A)/(2)+...

    Text Solution

    |

  10. If A+B+C=(pi)/(2), then prove that cos 2A + cos 2B + cos 2C=1+4 sin A ...

    Text Solution

    |

  11. If A+B+C=(pi)/(2), then prove that sin ^(2) A+ sin ^(2) B + sin ^(2) C...

    Text Solution

    |

  12. If A+B+C=(3pi)/(2), prove that cos 2A+ cos 2B+ cos 2C=1-4 sin A sin B ...

    Text Solution

    |

  13. If A+B+C=(3pi)/(2), prove that cos ^(2)A+ cos ^(2) B- cos ^(2)C=-2 cos...

    Text Solution

    |

  14. If A+B+C=0, then prove that cos ^(2)A+ cos ^(2) B + cos ^(2) C =1+2 co...

    Text Solution

    |

  15. If A+B+C = 2S , then P.T cos(S-A)+cos(S-B)+cos(S-C)+cosS=4cos.(A)/(...

    Text Solution

    |

  16. If A+B+C+D=360^(@), the prove that cos 2A + cos 2B + cos 2C + cos 2D =...

    Text Solution

    |

  17. Find the value of 2(sin^(6)theta+cos^(6)theta)-3(sin^(4)theta+cos^(4)t...

    Text Solution

    |

  18. Prove that (1+cot theta -"cosec" theta ) (1+ tan theta + sec theta )=2...

    Text Solution

    |

  19. If (2 sin theta )/(1+ cos theta + sin theta )=x, find the value of (1...

    Text Solution

    |

  20. Show that cos ^(4) alpha + 2 cos ^(2) alpha (1-(1)/(sec ^(2) alpha ))=...

    Text Solution

    |