Home
Class 10
MATHS
Prove that : (sectheta+tantheta-1)/(tant...

Prove that : `(sectheta+tantheta-1)/(tantheta-sectheta+1)=(costheta)/(1-sintheta)`

Text Solution

Verified by Experts

LHS `= (sec theta + tan theta -1)/(tan theta - sec theta +1) `
` = ((sec theta + tan theta)-(sec^(2)theta - tan^(2)theta))/((tan theta - sec theta +1)) " " [because sec^(2)theta - tan^(2)theta =1] `
`=((sec theta + tan theta)[1-(sec theta - tan theta)])/((tan theta - sec theta +1))`
`= ((sec theta + tan theta )(tan theta - sec theta +1))/((tan theta - sec theta +1))=(sec theta + tan theta)`
` =((1)/(cos theta)+(sin theta)/(cos theta))=((1+ sin theta)/(cos theta))=((1+ sin theta))/(cos theta) xx ((1- sin theta))/((1- sin theta)) `
` = ((1- sin^(2)theta))/(cos theta(1- sin theta)) = (cos^(2)theta)/(cos theta(1- sin theta))=(cos theta)/((1-sin theta))= RHS. `
Hence, ` (sec theta + tan theta -1)/(tan theta - sec theta +1)=(cos theta)/((1- sin theta)). `
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC IDENTITIES

    RS AGGARWAL|Exercise Exercise 13A|38 Videos

  • TRIGONOMETRIC IDENTITIES

    RS AGGARWAL|Exercise Exercise 13B|15 Videos

  • TRIANGLES

    RS AGGARWAL|Exercise Test Yourself|20 Videos

  • TRIGONOMETRIC RATIOS

    RS AGGARWAL|Exercise Exercise 10|35 Videos

Similar Questions

Explore conceptually related problems

(tantheta-sectheta)^2

tantheta-tantheta/2=sectheta/2

(tantheta+sectheta-1)/(tantheta-sectheta+1)=

(tantheta+sectheta-1)/(tantheta-sectheta+1)=

Prove that (tantheta+Sectheta+1)/(-tantheta+Sectheta+1)=(Costheta)/(1-Sintheta)

(sectheta+tantheta-1)(sectheta-tantheta+1)=

Prove that- (sectheta+tantheta)/(sec-tantheta)=((1+sintheta)/costheta)^2

Prove that- (sectheta+tantheta-1)/(1-sectheta+tantheta)=(1+sintheta)/costheta

Prove that (1+sectheta-tantheta)/(1+sectheta+tantheta) = (1-sintheta)/(costheta)

Pove that- sectheta-tantheta=1/(sectheta+tantheta)=(1-sintheta)/costheta

RS AGGARWAL-TRIGONOMETRIC IDENTITIES-Test Yourself
  1. Prove that : (sectheta+tantheta-1)/(tantheta-sectheta+1)=(costheta)/(1...

    Text Solution

    |

  2. (cos^(2)56^(@)+cos^(2)34^(@))/(sin^(@)56^(@)+sin^(2)34^(@))+3tan^(2)56...

    Text Solution

    |

  3. (sin^2 30^@ cos^2 45^@+4 tan^2 30^@+1/2 sin^2 90^@+1/8 cot^2 60^@)=?

    Text Solution

    |

  4. If cosA+cos^(2)A=1, then sin^(2)A+sin^(4)A=?.

    Text Solution

    |

  5. If sin theta=(sqrt(3))/(2)" then " ("cosec"theta+cot theta)=?

    Text Solution

    |

  6. If cotA=(4)/(5), then ((sinA+cosA))/((sinA-cosA))=?

    Text Solution

    |

  7. If 2x=secA and (2)/(x)=tanA, " prove that " (x^(2)-(1)/(x^(2)))=(1)/(4...

    Text Solution

    |

  8. If sqrt(3) tantheta=3sintheta, " prove that " (sin^(2)theta-cos^(2)the...

    Text Solution

    |

  9. Prove that ((sin^(2)73^(@)+sin^(2)17^(@)))/((cos^(2)28^(@)+cos^(2)62^(...

    Text Solution

    |

  10. If 2sin2 theta=sqrt(3) ,then the value of theta is :

    Text Solution

    |

  11. Prove that sqrt((1+cosA)/(1-cosA))=("cosec"A+cotA).

    Text Solution

    |

  12. If cosec theta + cot theta= p, cos theta = ?

    Text Solution

    |

  13. Prove that ("cosec"A-cotA)^(2)=((1-cosA))/((1+cosA)).

    Text Solution

    |

  14. If 5cottheta=3. find the value of (5sintheta-3costheta)/(4sintheta+3co...

    Text Solution

    |

  15. Prove that (sin32^(@)cos58^(@)+cos32^(@)sin58^(@))=1.

    Text Solution

    |

  16. If x=a sin theta+b cos theta and y=a cos theta -b sin theta, " prove t...

    Text Solution

    |

  17. ((1+sintheta))/((1-sintheta))=?

    Text Solution

    |

  18. Prove that (1)/((sec theta - tan theta))-(1)/(cos theta)=(1)/(cos th...

    Text Solution

    |

  19. ((sinA-2sin^(3)A))/((2cos^(3)A-cosA)) = ?

    Text Solution

    |

  20. Prove that (tanA)/((1-cotA))+(cotA)/((1-tanA))=(1+tanA+cotA).

    Text Solution

    |

  21. If sec5A="cosec"(A-36^(@)) and 5A " is an acute angle, show that " A=2...

    Text Solution

    |