Home
Class 10
MATHS
Prove that if two angles alphaandbeta ar...

Prove that if two angles `alphaandbeta` are complementary angles, then
`cotbeta+cosbeta=(cosbeta)/(cosalpha)(1+sinbeta)`

Text Solution

Verified by Experts

LHS `=cotbeta+cosbeta=(cosbeta)/(sinbeta)+cosbeta=(cosbeta)/(sin(90^(@)-alpha))+cosbeta`.
`=(cosbeta)/(cosalpha)+cosbeta=(cosbeta)/(cosalpha)(1+cosalpha)`
`=(cosbeta)/(cosalpha){1+cos(90^(@)-beta)}=(cosbeta)/(cosalpha)(1+sinbeta)`
Hence `cotbeta+cosbeta=(cosbeta)/(cosalpha)(1+sinbeta)`.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS OF COMPLEMENTARY ANGLES

    CALCUTTA BOOK HOUSE|Exercise EXERCISE|28 Videos

  • TRIGONOMETRIC RATIOS AND TRIGONOMETRIC IDENTITIES

    CALCUTTA BOOK HOUSE|Exercise EXERCISE|66 Videos

  • VARIATION

    CALCUTTA BOOK HOUSE|Exercise EXERCISE|59 Videos

Similar Questions

Explore conceptually related problems

If alpha and beta are complementary angles, then show that cot beta+cos beta= (cos beta)/(cos alpha) (1+sin beta) .

Prove that if two angles alphaandbeta are complementary angles, then sin^(2)alpha+sin^(2)beta=1

Prove that if two angles alphaandbeta are complementary angles, then (secalpha)/(cosalpha)-cot^(2)beta=1

If alpha+beta=90^(@) , then find the value of cotbeta+cosbeta-(cosbeta)/(cosalpha)(1+sinbeta)

(cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2 =

Fill in the blanks: If A and B are complementary angles then sin A =__.

Complementary angle of 27∘27'27" is

By geometrical interpretation, prove that (i) sin(alpha+beta)=sin alpha cos beta+sinbeta cosalpha (ii) cos(alpha+beta)=cosalpha cosbeta -sin alpha sinbeta

Prove that if one of the angles of a parallelogram be a right -angle , then it should be a rectangle.

Prove that |cosalpha-cosbeta|lt=|alpha-beta|

CALCUTTA BOOK HOUSE-TRIGONOMETRIC RATIOS OF COMPLEMENTARY ANGLES -EXERCISE
  1. Prove that if two angles alphaandbeta are complementary angles, then ...

    Text Solution

    |

  2. If A, B, C are the angles of a triangle then tan ((B+C)/2)=

    Text Solution

    |

  3. (sin21^(@)30')/(cos68^(@)30')

    Text Solution

    |

  4. (sin52^(@)+cos38^(@))/(sin38^(@)+cos52^(@))

    Text Solution

    |

  5. If sec9theta=cosec9theta, then the value of theta is equal to

    Text Solution

    |

  6. If the sum of any two acute angles be 180^(@), then they are called cm...

    Text Solution

    |

  7. If sin(theta+36^(@))=costheta then the value of theta" is "27^(@)

    Text Solution

    |

  8. The complementary angle of 90^(@) is

    Text Solution

    |

  9. If in DeltaABC,angleC=90^(@) then 1+tan^(2)A

    Text Solution

    |

  10. If theta=0^(@) then the trigonometrical ratio tangent of complementary...

    Text Solution

    |

  11. Find the value of cos1^(@)cos2^(@)cos3^(@).............cos180^(@)

    Text Solution

    |

  12. If 0^(@)angletheta angle20^(@), then find the value of theta when sin^...

    Text Solution

    |

  13. If sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/(2), then then the value of (x...

    Text Solution

    |

  14. If X, Y, Z are the angles of a DeltaXYZ then prove that cos^(2)""(X)/...

    Text Solution

    |

  15. If x=acos(90^(@)-theta)andy=bcot(90^(@)-theta), then prove that (a^(2)...

    Text Solution

    |

  16. Prove that (1+sec22^(@)+cot68^(@))(1-cosec22^(@)+tan68^(@))=2

    Text Solution

    |

  17. If angleA+angleB=90^(@) then prove that 1+(cotA)/(cotB)=cosec^(2)A

    Text Solution

    |

  18. If alpha+beta=90^(@), then find the value of cotbeta+cosbeta-(cosbeta)...

    Text Solution

    |

  19. Find the value of (5sin75^(@)sin77^(@)+2cos13^(@)cos15^(@))/(cos15^(@)...

    Text Solution

    |

  20. If alpha+beta=90^(@) then prove that cosec^(2)alpha+cosec^(2)beta=cose...

    Text Solution

    |

  21. Prove that sec^(2)11^(@)-(1)/(tan^(2)79^(@))=1.

    Text Solution

    |