Home
Class 11
MATHS
If tan alpha= n tan beta and sin alpha= ...

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

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 cos (theta + 2alpha) = m cos theta , prove that : cot alpha = (1+m)/(1-m)tan(theta + alpha) .

If (sin beta)/(sin(2 alpha+ beta))=m/n , prove that : cot (alpha+ beta)= (n-m)/(n+m) cot alpha .

If (cos^4 alpha)/(cos^2 beta)+ (sin^4 alpha)/(sin^2 beta) =1 , prove that : (cos^4 beta)/(cos^2 alpha)+ (sin^4 beta)/ (sin^2 alpha) =1 .

If (cos^4 alpha)/(cos^2 beta)+ (sin^4 alpha)/(sin^2 beta) =1 , prove that : sin^4 alpha+ sin^4 beta= 2 sin^2 alpha sin^2 beta .

If alpha and beta satisfying 2 sec2 alpha = tan beta + cot beta , then alpha+beta =

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 2 tan^2 alpha tan^2 beta tan^2 gamma+ tan^2 alpha tan^2 beta+ tan^2 beta tan^2 gamma+ tan^2 gamma tan^2 alpha=1 , prove that sin^2 alpha+ sin^2 beta+ sin^2 gamma =1 .

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

If m tan(alpha-theta)/( cos^2 theta) = n (tan theta)/ (cos^2 (alpha - theta) the prove that 2 theta = alpha - [ tan^(-1) ((n-m)/(n+m)) tan alpha]

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

MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. If x=r sin theta cos phi, y= r sin theta sin phi, z=r cos theta, prov...

    Text Solution

    |

  2. If (sin A)/(sin B)=m, and (cosA)/(cosB)=n, prove that tan A= +- m/n sq...

    Text Solution

    |

  3. If tan alpha= n tan beta and sin alpha= m sin beta, prove that cos^2 a...

    Text Solution

    |

  4. Which of the six t-ratios are positive for the angle : 210^@ ?

    Text Solution

    |

  5. Which of the six t-ratios are positive for the angle : -405^@ ?

    Text Solution

    |

  6. If sin theta= -1/sqrt2 and tan theta=1, find the quadrant in which the...

    Text Solution

    |

  7. Prove that sectheta+costheta can never be equal to (3)/(2).

    Text Solution

    |

  8. Prove that : cosec^2 theta+ sin^2 theta can never be less than 2.

    Text Solution

    |

  9. Is the equation 2 cos^2 theta + cos theta-6 = 0 possible ?

    Text Solution

    |

  10. Is the equation 2 sin^2 theta -cos theta+ 4 = 0 possible ?

    Text Solution

    |

  11. Find the values of the remaining functions in the following problem : ...

    Text Solution

    |

  12. Find the values of other five trignometrtic functions in each of the f...

    Text Solution

    |

  13. Find the values of the remaining functions in the following problem : ...

    Text Solution

    |

  14. Find the values of the remaining functions in the following problem : ...

    Text Solution

    |

  15. Find the values of the remaining functions in the following problem : ...

    Text Solution

    |

  16. Find the values of the remaining functions in the following problem : ...

    Text Solution

    |

  17. Find the values of the remaining functions in the following problem : ...

    Text Solution

    |

  18. Find the values of the remaining functions in the following problem : ...

    Text Solution

    |

  19. Find the values of the remaining functions in the following problem : ...

    Text Solution

    |

  20. If cos A=21/29 and A lies in the fourth quadrant, find sin A and tan A...

    Text Solution

    |