Home
Class 12
MATHS
If A+B+C=0, then prove that cos ^(2)A+ c...

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

Text Solution

Verified by Experts

The correct Answer is:
`=1+2 cos A cos B cos C= 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=(3pi)/(2) , prove that cos ^(2)A+ cos ^(2) B- cos ^(2)C=-2 cos A cos B sin C.

If A+B+C=180^(@) then prove that cos^(2)A+cos^(2)B-cos^(2)C=1-2sin A sin B cos C

If A+B+C=180^(@) then prove that cos^(2)A+cos^(2)B+cos^(2)C=1-2cosAcosBcosC

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=90^(@) " then " cos^(2) A + cos^(2) B + cos^(2) C =

If A+B+C+D=360^(@) , the prove that cos 2A + cos 2B + cos 2C + cos 2D =4 cos (A+B) cos (A+C) cos (A+D)

SRISIRI PUBLICATION-TRIGONOMETRIC RATIONS, TRANSFORMATIONS-LAQ
  1. If A+B+C=(3pi)/(2), prove that cos 2A+ cos 2B+ cos 2C=1-4 sin A sin B ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. For what values of x in the first quadrant (2 tan x)/( 1- tan ^(2) x) ...

    Text Solution

    |

  11. If A,B,C,D are the angles of a cyclic quadrilateral then cos A + cos...

    Text Solution

    |

  12. Express cos^(6)A + sin^(6)A interms of sin 2A.

    Text Solution

    |

  13. Prove that sin ^(2) ((pi)/(8)+(A)/(2)) - sin ^(2) ((pi)/(8) - (A)/(2))...

    Text Solution

    |

  14. Expres sqrt3 sin 0 + cos 0 as a sine of an angle .

    Text Solution

    |

  15. Simplify tan ((pi)/(4) +A) tan ((pi)/(4)-A)

    Text Solution

    |

  16. Find the value of tan 75^(@) + cot 75^(@)

    Text Solution

    |

  17. If tan theta =(cos 11^(@) + sin 11^(@) )/( cos 11^(@)- sin 11^(@)) and...

    Text Solution

    |

  18. If sin A=(12)/(13), cos B= (3)/(5) and neither A nor B is in the first...

    Text Solution

    |

  19. If 0 lt A, B lt 90^(@), cos A= (5)/(13) and sin B =(4)/(5) then find s...

    Text Solution

    |

  20. If sin =(1)/(sqrt10), sin beta =(1)/(sqrt5) and alpha , beta are acu...

    Text Solution

    |