Home
Class 11
MATHS
If (tan (theta+alpha))/a= (tan (theta+be...

If `(tan (theta+alpha))/a= (tan (theta+beta))/b= (tan (theta+ gamma))/c`, prove that : `(a+b)/(a-b) sin^2 (alpha- beta) +(b+c)/(b-c) sin^2 (beta-gamma)+ (c+a)/(c-a) sin^2 (gamma-alpha)=0` .

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 2 tan beta+cot beta= tan alpha , prove that cot beta= 2 tan (alpha-beta) .

If theta+phi= alpha and tan theta=k tan phi , prove that : sin alpha=(k+1)/(k-1) sin (theta-phi) .

If a tan alpha+b tan beta=(a+b) tan ((alpha+beta)/2) , where alpha ne beta , prove that : a cos beta= b cos alpha .

If tan beta= (Q sin alpha)/(P+Q cos alpha) , prove that : tan (alpha-beta)= (P sin alpha)/(Q+P cos alpha) .

If tan theta =a/b , prove that a sin 2 theta+b cos 2 theta=b .

If alpha and beta are distinct roots of the equation : a tan theta+b sec theta=c , prove that tan (alpha+ beta)= (2ac)/(a^2-c^2) .

If alpha and beta are the solutions of a cos theta+b sin theta=c , then prove that : cos (alpha- beta)= (2c^2- (a^2+b^2))/(a^2+b^2) .

If cos(theta-alpha) = a and cos(theta-beta) = b then the value of sin^2(alpha-beta) + 2ab cos(alpha-beta)

If tan alpha= n tan beta and sin alpha= m sin beta , prove that cos^2 alpha= (m^2-1)/(n^2-1) .

If alpha and beta are two real numbers satisfying the equation a cos x + b sin x = c, prove that : tan (alpha+ beta)= (2ab)/(a^2-b^2) .

MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. If (tan (theta+alpha))/a= (tan (theta+beta))/b= (tan (theta+ gamma))/c...

    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

    |