Home
Class 12
MATHS
If A +B+C= 2S , then prove that (i) si...

If `A +B+C= 2S `, then prove that
(i) `sin (S-A)+sin (S-B) + sin C=4 cos . (S-A)/(2) cos. (S-B)/(2) sin .(C)/(2)`
(ii) `cos (S-A)+cos (S-B)+cos C=-1+4 cos. (S-A)/(2) cos.(S-B)/(2)cos. (C)/(2)`

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIONS, TRANSFORMATIONS

    SRISIRI PUBLICATION|Exercise VSAQ|51 Videos

  • TRIGONOMETRIC RATIONS, TRANSFORMATIONS

    SRISIRI PUBLICATION|Exercise LAQ|64 Videos

  • TRIGONOMETRIC EQUATIONS

    SRISIRI PUBLICATION|Exercise SPQ|8 Videos

Similar Questions

Explore conceptually related problems

If A+B+C = 2S , then prove that sin(S-A)+sin(S-B)+sinC = 4 cos ((S-A)/2) cos ((S-B)/2) sin C/2 .

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)

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

If A+B+C=2S then prove that the following: cos(S-A)+cos(S-B)+cosC =4cos((S-A)/2)cos((S-B)/2)cosC/2-1

If A+B+C= 2S , " then " sin (S-A) sin(S-B) + sinS sin(S-C)=

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

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

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)

In triangle ABC , prove that sin .(A)/(2)+ sin. (B)/(2) -sin. (C)/(2)=-1+4 cos.(pi-A)/(4)cos. (pi-B)/(4)sin. (pi-C)/(4)

SRISIRI PUBLICATION-TRIGONOMETRIC RATIONS, TRANSFORMATIONS-LAQ
  1. If A +B+C= 2S , then prove that (i) sin (S-A)+sin (S-B) + sin C=4 co...

    Text Solution

    |

  2. If A+B+C= 180^(@), then show that sin 2A+ sin 2B+ sin 2C =4 sin A sin...

    Text Solution

    |

  3. If A, B, C are angles of a triangle, then S. T sin 2A -sin 2B + sin...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |