Home
Class 11
MATHS
If alpha and beta are the solutions of a...

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)`.

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 alpha and beta are the solution of a cos theta + b sin theta = c , then

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 two real numbers such that alpha- beta ne 2 n pi , n is integer which satisfy the equation a cos phi + b sin phi =c , then prove that: cos (alpha+ beta)= (a^2-b^2)/(a^2+b^2) .

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

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) .

If acos theta-b sin theta=c , show that asin theta+b cos theta=+-sqrt(a^2+b^2-c^2dot)

If x cos theta- y sin theta=a,x sin theta+ y cos theta=b , prove that x^2+y^2= a^2+b^2 .

If cosec theta- sin theta= a^3, sec theta- cos theta= b^3 , prove that a^2b^2(a^2+b^2)=1 .

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

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

MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. If a tan alpha+b tan beta=(a+b) tan ((alpha+beta)/2), where alpha ne b...

    Text Solution

    |

  2. If alpha and beta are the solution of a cos theta + b sin theta = c...

    Text Solution

    |

  3. If alpha and beta are the solutions of a cos theta+b sin theta=c, the...

    Text Solution

    |

  4. If alpha and beta are distinct roots of the equation : a tan theta+b s...

    Text Solution

    |

  5. Prove that cot 7 1^@/2 = (1+cos15^@)/(sin 15^@).

    Text Solution

    |

  6. Prove that 4 cos 36^@ +cot 7 1^@/2 = sqrt1+sqrt2 +sqrt3+ sqrt4+ sqrt5+...

    Text Solution

    |

  7. Prove that tan 82 (1(0))/(2)=(sqrt(3)+sqrt(2))(sqrt(2)+1) or cot 7 (...

    Text Solution

    |

  8. Prove that 4 sin 27^@ = sqrt(5+sqrt5)+sqrt(3-sqrt5).

    Text Solution

    |

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

    Text Solution

    |

  10. Prove that cot theta cot 2 theta+ cot 2 theta cot 3 theta+ 2= cot thet...

    Text Solution

    |

  11. Prove that: (cos 2A cos 3A-cos 2A cos 7A + cos A cos 10A)/(sin 4A sin ...

    Text Solution

    |

  12. If (sin (theta+alpha))/(cos (theta-alpha))= (1-m)/(1+m), prove that : ...

    Text Solution

    |

  13. If theta(1),theta(2),theta(3),".......",theta(n) are in AP whose commo...

    Text Solution

    |

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

    Text Solution

    |

  15. In any triangle ABC, prove that : sin frac (A)(2) +sin frac (B)(2)+s...

    Text Solution

    |

  16. In any triangle ABC, prove that : cos frac (A)(2) +cos frac (B)(2)+c...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |