Home
Class 12
MATHS
If alpha, beta are acute angles and cos ...

If `alpha, beta` are acute angles and `cos 2alpha = (3cos2beta -1)/(3-cos2 beta)` prove that `tan alpha tan beta= sqrt2 :1`.

Promotional Banner

Topper's Solved these Questions

  • Circular Functions, Identities

    A DAS GUPTA|Exercise Exercise|300 Videos

  • Circles

    A DAS GUPTA|Exercise EXERCISE|122 Videos

  • COMPLEX NUMBERS

    A DAS GUPTA|Exercise EXERCISE|224 Videos

Similar Questions

Explore conceptually related problems

If alpha and beta are acute angles and cos2 alpha=(3cos2 beta-1)/(3-cos2 beta). Prove that :tan alpha=sqrt(2)tan beta

alpha and beta are acute angles and cos2 alpha=(3cos2 beta-1)/(3-cos2 beta) then tan alpha cot beta=

cos 2 alpha =(3 cos 2 beta -1)/( 3-cos 2 beta), then tan alpha=

If alpha and beta be acute angles and cos2 alpha=(3cos2 beta-1)/(3-cos2 beta), then tan alpha is :

If cos2alpha=(3cos2beta-1)/(3-cos2beta) , then tan alpha is equal to

If alpha and beta are acute angles satisfying cos2 alpha=(3cos2 beta-1)/(3-cos2 beta), then tan alpha=sqrt(2)tan beta (b) (1)/(sqrt(2))tan beta(c)sqrt(2)cot beta(d)(1)/(sqrt(2))cot beta

If alpha and beta are positive.acute angles and cos2 alpha=(n cos2 beta-1)/(n-cos2 beta)(n<1), show that sqrt(n-1)tan alpha=sqrt(n+1)tan beta

If alpha,beta,gamma are acute angle such that cos alpha=tan beta,cos beta=tan gamma and cos gamma=tan alpha then

sin alpha sin beta-cos alpha cos beta=1 then show that tan alpha+tan beta=0

A DAS GUPTA-Circular Functions, Identities -Exercise
  1. If f(x) = 3(sin x - cos x)^(4) + 6(sin x + cos x)^(2) +4(sin^(6)x + co...

    Text Solution

    |

  2. Prove that 1 + cos 2x + cos 4x + cos 6x = 4 cos x *cos 2x *cos 3x.

    Text Solution

    |

  3. If alpha, beta are acute angles and cos 2alpha = (3cos2beta -1)/(3-cos...

    Text Solution

    |

  4. If tan theta* tan phi = sqrt((x-y)/(x+y)) prove that (x - y cos 2the...

    Text Solution

    |

  5. If x in (pi, 2pi), prove that ((sqrt(1+cosx))+(sqrt(1-cos x)))/((sqrt(...

    Text Solution

    |

  6. Show that cot theta* cot 2theta+ cot 2theta *cot 3theta + 2 = cot thet...

    Text Solution

    |

  7. Prove that sin x* sin y*sin(x - y) + sin y *sin z*sin(y- z) + sin z ...

    Text Solution

    |

  8. Prove that (3 + cos 4theta) cos 2theta = 4(cos^(8)theta - sin^(8)theta...

    Text Solution

    |

  9. Prove that cos^(2)theta + cos^(2)(alpha + theta) – 2cos alpha *cos th...

    Text Solution

    |

  10. If sin beta = 1/5 sin(2alpha +beta), show that tan(alpha +beta) = 3/2...

    Text Solution

    |

  11. If Tn = sin^(n)theta + cos^(n)theta then prove that (T5 -T3): (T7- T5...

    Text Solution

    |

  12. If f(alpha, beta) = cos^(4)alpha/cos^(2)beta + sin^(4)alpha/sin^(2)bet...

    Text Solution

    |

  13. If cos A = tan B, cos B = tan C and cos C = tan A then show that sin A...

    Text Solution

    |

  14. Prove that cos theta =(cos alpha- cos beta)/(1 -cos alpha*cos beta) ⇔ ...

    Text Solution

    |

  15. If sqrt(a + b) tan = theta/2 = sqrt(a -b) tan phi/2 then prove that a ...

    Text Solution

    |

  16. If sin theta - sin phi = a and cos theta + cos phi = b then prove tha...

    Text Solution

    |

  17. If sin x + sin y + sin z = 0 and cos x + cos y + cos z = 0 then prove...

    Text Solution

    |

  18. If sin alpha + sin beta =p, cos alpha + cos beta = q then find the va...

    Text Solution

    |

  19. If cos(x - y)= -1, show that cos x + cos y = 0 and sin x + sin y = 0.

    Text Solution

    |

  20. If alpha, beta be the solutions of theta for the equation a tan theta...

    Text Solution

    |