Home
Class 11
MATHS
If A + B + C =180^@, prove that : sin^2...

If `A + B + C =180^@`, prove that :
`sin^2 A+ sin^2 B+sin^2 C=2 (1+cos A cos B cos C)`.

Promotional Banner

Topper's Solved these Questions

  • TRIGNOMETRY

    MODERN PUBLICATION|Exercise EXERCISE|730 Videos

  • STRAIGHT LINES

    MODERN PUBLICATION|Exercise EXERCISE|304 Videos

Similar Questions

Explore conceptually related problems

If A + B + C =180^@ , prove that : sin^2 A- sin^2 B+ sin^2 C=2 sin A cos B sinC .

If A + B + C =180^@ , prove that : sin^2 A+ sin^2 B-sin^2 C=2 sin A sin B cos C .

If A + B + C =180^@ , prove that : cos^2 A+ cos^2 B+cos^2 C=1-2 cos A cos B cosC .

If A + B + C =180^@ , prove that : cos^2 A+ cos^2 B-cos^2 C= 1-2 sin A sin B cos C .

If A + B + C =180^@ , prove that : cos^2 A- cos^2 B-cos^2 C=2 cos A sin B sinC -1 .

If A + B + C =pi/2 , prove that : sin^2 A +sin^2 B+sin^2 C= 1-2 sin A sin B sin C .

If A + B + C =360^@ , prove that : 1-cos^2 A-cos^2 B-cos^2 C+2 cos A cosB cos C=0 .

If A + B + C =pi , prove that : (sin 2A + sin 2B + sin 2C)/(cos A + cos B + cos C-1)= 8 cos frac (A)(2) cos frac (B)(2) cos frac (C)(2) .

Prove that : sin^2 A=cos^2 (A-B)+ cos^2 B-2 cos (A - B) cos A cos B .

If A + B + C =pi , prove that : cos 2A + cos 2B + cos 2C = -1-4 cos A cos B cos C .

MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. If A + B + C =180^@, prove that : sin^2 A+ sin^2 B+sin^2 C=2 (1+cos A...

    Text Solution

    |

  2. Find the radian measure corresponding to the following degree measure ...

    Text Solution

    |

  3. Find the radian measure corresponding to the following degree measure ...

    Text Solution

    |

  4. Find the radian measure corresponding to the following degree measure ...

    Text Solution

    |

  5. Find the radian measures corresponding to the following degree measure...

    Text Solution

    |

  6. Find the radian measure corresponding to the following grade measure :...

    Text Solution

    |

  7. Find the radian measure corresponding to the following grade measure :...

    Text Solution

    |

  8. Find the radian measure corresponding to the following grade measure :...

    Text Solution

    |

  9. Find thedegree measure corresponding to the following measure. (Use pi...

    Text Solution

    |

  10. Find thedegree measure corresponding to the following measure. (Use pi...

    Text Solution

    |

  11. Find thedegree measure corresponding to the following measure. (Use pi...

    Text Solution

    |

  12. Find thedegree measure corresponding to the following measure. (Use pi...

    Text Solution

    |

  13. The angles of a triangle are3x^@, ((4x)/3)^g and (2 pi x)/75 radians. ...

    Text Solution

    |

  14. Express the radians the fourth angle of a quadrilateral which has thre...

    Text Solution

    |

  15. The sum of two angles is 80 grades and their difference is 18^@. Find ...

    Text Solution

    |

  16. The angles of a triangle are in the ratio 1 : 2: 3. Find the angles in...

    Text Solution

    |

  17. The vertical angle of an isosceles triangle is 2/3 rd of each of its b...

    Text Solution

    |

  18. In a right-angled triangle, the difference between two acute angles is...

    Text Solution

    |

  19. The wheel of a carriage is 91 cm in diameter and makes 5 revolutions p...

    Text Solution

    |

  20. A wheel makes 360 revolutions in one minute. Through how many radians ...

    Text Solution

    |

  21. Find the length of the arc of a circle of radius 5 cm subtending an an...

    Text Solution

    |