Home
Class 11
MATHS
If A + B + C =180^@, prove that : cos (-...

If `A + B + C =180^@`, prove that : `cos (-A+B +C)+cos(A-B+C)+ cos (A +B-C)=1+ 4cos 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

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

Prove that : cos (A + B) cos (A - B) = cos^2A-1+ cos^2B .

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=1-2 cos A cos B cosC .

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

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 =2S, prove that : cos^2 S + cos^2 (S- A) + cos^2 (S-B)+ cos^2 (S -C) = 2 +2 cos A cos B cos C .

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

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

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

MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. In any triangle ABC, prove that : cos frac (A)(2) +cos frac (B)(2)+c...

    Text Solution

    |

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

    Text Solution

    |

  3. If A + B + C =180^@, prove that : cos (-A+B +C)+cos(A-B+C)+ cos (A +B-...

    Text Solution

    |

  4. If A + B + C =180^@, prove that : sin (B+C-A) + sin(C+ A-B)+ sin(A +B-...

    Text Solution

    |

  5. If in triangle ABC, cot A + cot B + cot C = sqrt3, prove that the tria...

    Text Solution

    |

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

    Text Solution

    |

  7. If A+B +C =2S, prove that : sin (S - A) + sin (S- B) + sin (S-C)-sinS=...

    Text Solution

    |

  8. If A+B +C =2S, prove that : cos^2 S + cos^2 (S- A) + cos^2 (S-B)+ cos^...

    Text Solution

    |

  9. If x +y+ z=xyz, prove that : (2x)/(1-x^2)+(2y)/(1-y^2)+(2z)/(1-z^2)= ...

    Text Solution

    |

  10. If x +y+ z=xyz, prove that : (3x-x^3)/(1-3x^2)+ (3y-y^3)/(1-3y^2)+(3z...

    Text Solution

    |

  11. If xy + yz + zx = 1, prove that : x/(1-x^2)+y/(1-y^2)+z/(1-z^2)= (4xy...

    Text Solution

    |

  12. Find the solutions x in [0,2 pi] of : sin 2x-12 (sin x -cos x) + 12 =...

    Text Solution

    |

  13. Solve the following trigonometric equation : cos 3 theta + 8cos^3 th...

    Text Solution

    |

  14. If tan(pi cos theta )= cot (pi sin theta ) ,then cos^(2)(theta -pi/...

    Text Solution

    |

  15. Find all the solution of 4 cos^(2)x sinx -2 sin^(2) x=3 sinx

    Text Solution

    |

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

    Text Solution

    |

  17. Find the radian measure of the following degree measure 40°20

    Text Solution

    |

  18. Radian measures of 520^(@) is :

    Text Solution

    |

  19. The value of (25)^0 is :

    Text Solution

    |

  20. Find the value of : sin 765^@.

    Text Solution

    |