Home
Class 10
MATHS
If sec(90^@ - alpha) = 4 - cosec alpha (...

If `sec(90^@ - alpha) = 4 - cosec alpha (0^@ < alpha < 90^@)`, then the value of x is

A

`75^@`

B

`60^@`

C

`45^@~

D

`30^@`

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 2sec^2 alpha- sec^4 alpha-2 cosec^2 alpha+cosec^4 alpha=15/4 then tan alpha=

If 0 < alpha < pi/ 6 then alpha(cosec alpha) is

If sec alpha and cosec alpha are the roots of x^2-px+q=0 then prove that p^2=q(q+2)

If sec alpha and "cosec" alpha are the roots of x^(2)- px+q=0 then show that p^(2)=q(q+2)

If p and q are the lengths of the perpendiculars from the origin to the straight lines x "sec" alpha + y " cosec" alpha = a " and " x "cos" alpha-y " sin" alpha = a "cos" 2alpha, " then prove that 4p^(2) + q^(2) = a^(2).

Prove that : sec alpha+ sec (120^(@)+ alpha) sec (120^(@)-alpha)=-3 sec 3 alpha

1/(cos alpha + cos 3 alpha)+ 1/(cos alpha + cos 5 alpha)+ 1/(cos alpha + cos 7 alpha) +....+ 1/(cos alpha +cos(2n+1) alpha) = 1/2 "cosec" alpha[tan (n+1) alpha - tan alpha ]

If alpha+beta = 90^@ , prove that sec^2 alpha+sec^2 beta = sec^2 alpha sec^2 beta .

Prove the following identities: sec(alpha + beta) = (sec alpha sec beta)/(1 - tan alpha tan beta)

If the line x cos alpha+ y sin alpha=p be a normal to the hyperbola b^(2)x^(2)-a^(2)y^(2)=a^(2)b^(2), show that, p^(2)(a^(2) sec ^(2) alpha- b^(2)"cosec"^(2) alpha)=(a^(2)+b^(2))^(2)

UNITED BOOK HOUSE-Trigonometric Ratios of Complementry Angle-Exercise
  1. If tan 2alpha = cot 2beta, then sec(alpha + beta) =

    Text Solution

    |

  2. If tan 2theta . Tan 3 theta =1, then sin5theta =

    Text Solution

    |

  3. If sec(90^@ - alpha) = 4 - cosec alpha (0^@ < alpha < 90^@), then the ...

    Text Solution

    |

  4. Calculate the slope of a line, that passes through the origin, and the...

    Text Solution

    |

  5. Sin 2A = 2sin A is true when A =

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. (2 tan 30^@)/(1 - tan^2 30^@) is equal to

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. (1 + sec 20^@ + cot 70^@) (1 - cosec 20^@ + tan 70^@) equals

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |