Home
Class 10
MATHS
alpha, beta are positive acute angle and...

`alpha, beta` are positive acute angle and `sec^2 alpha - cot^2 (beta/2) = 1`, then___

A

`alpha = beta`

B

`alpha + beta = Pi/2`

C

`alpha + 2beta = Pi`

D

`2alpha + beta = Pi`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • Trigonometric Rations and Trigonometric Identities

    UNITED BOOK HOUSE|Exercise Exercise |31 Videos
  • Trigonometry : Concept of Measurement of Angle

    UNITED BOOK HOUSE|Exercise Exercise |24 Videos

Similar Questions

Explore conceptually related problems

If alpha and beta are positive acute angles and cos2alpha=(3cos2beta-1)/(3-cos2beta) ,then prove that tan alpha=sqrt2tanbeta

If" "alpha " and " beta are positive acute angles and cos 2 alpha = (3 cos 2 beta-1)/(3-cos 2 beta),"show that", tan alpha = sqrt2 tan beta

If " "alpha " and " beta " are positive acute angles and " cos 2 alpha = (n cos 2 beta-1)/(n- cos 2 beta) (n>1), show that sqrt (n-1)tan alpha = sqrt(n+1) tan beta.

If alpha , beta positive acute angles and sec(alpha+beta)-sec(alpha-beta)=2 cosec alpha show that sinalpha=cos (beta/2)-sin(beta/2)

If sin alpha = 1/sqrt10, cos beta = 2/sqrt5 "and" alpha, beta are positive acute angles, then find the value of (alpha + beta)

If alpha, beta, gamma ,are positive acute angles and sin (alpha+beta-gamma)=cos(beta+gamma-alpha)=tan (gamma+alpha-beta)=1 find alpha,beta and gamma .

If sin alpha=(12)/(13), cos beta =4/5 and alpha, beta are two acute angles, then Value of sec alpha cot beta +tanalpha cosec beta is

If alpha and beta are complementery angles, then the value of sec^2 alpha - cot^2 beta is

UNITED BOOK HOUSE-Trigonometric Ratios of Complementry Angle-Exercise
  1. Sin 2A = 2sin A is true when A =

    Text Solution

    |

  2. It A + B = 90^@, then (tan A tan B + tan A cot B)/(sin A sec B) - (sin...

    Text Solution

    |

  3. If tan A = cot B, then prove that A + B = 90°.

    Text Solution

    |

  4. (sin^2 22^@ + sin^2 68^@ + cot^2 68^@) equals

    Text Solution

    |

  5. (2 tan 30^@)/(1 - tan^2 30^@) is equal to

    Text Solution

    |

  6. If theta and (2theta - 45^@) are acute angles such that cosec theta co...

    Text Solution

    |

  7. A, B and C are interior angles of a triangle ABC, then sin ((B + C)/(2...

    Text Solution

    |

  8. The value of tan 10^@ tan 15^@ 75^@ tan 80^@ is

    Text Solution

    |

  9. If 5theta and 4theta are acute angles satisfying sin 5theta = cos 4the...

    Text Solution

    |

  10. [sin^2 1^@ + sin^2 2^@ +sin^2 3^@ + ……………….. + sin^2 87^@ + sin^2 88^@...

    Text Solution

    |

  11. (sin^2 1^@ + sin^2 3^@ + sin^2 5^@ + ………………… + sin^2 85^@ + sin^2 87^@...

    Text Solution

    |

  12. The value of (cos(90^@ - theta)sec(90^@ - theta) tan theta)/(cosec(90^...

    Text Solution

    |

  13. The value of (tan 47^@ + cot 27^@)/(tan 43^@ + cot 63^@) is

    Text Solution

    |

  14. (1 + sec 20^@ + cot 70^@) (1 - cosec 20^@ + tan 70^@) equals

    Text Solution

    |

  15. alpha, beta are positive acute angle and sec^2 alpha - cot^2 (beta/2) ...

    Text Solution

    |

  16. ABCD is a cyclic quadrilateral and tan (A/2) tan (C/2) + tan (B/2) tan...

    Text Solution

    |

  17. If cos (67^@30') = x and cosec (22^@30') = y then which is true?

    Text Solution

    |

  18. If cosec 39^@ = x, the value of (1)/(cosec^2 51^@) + sin^2 39^@ + tan^...

    Text Solution

    |

  19. sin^2 5^@+sin^2 10^@ + sin^2 15^@+.........+sin^2 85^@+sin^2 90^@ equa...

    Text Solution

    |

  20. If A, B and C are three angles of a triangle, then the incorrect relat...

    Text Solution

    |