Home
Class 10
MATHS
Prove that : sqrt((1-cos^(2)theta)sec^(...

Prove that : `sqrt((1-cos^(2)theta)sec^(2)theta)=tantheta`

Text Solution

Verified by Experts

L.H.S. `=sqrt((1-cos^(2)theta)sec^(2)theta)=sqrt(sin^(2)theta*(1)/(cos^(2)theta))=sqrt(sin^(2)theta/(cos^(2)theta))`
`=sqrt(tan^(2)theta)=tan theta=R.H.S.`
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO TRIGONOMETRY

    NAGEEN PRAKASHAN|Exercise Exercise 8a|20 Videos

  • INTRODUCTION TO TRIGONOMETRY

    NAGEEN PRAKASHAN|Exercise Exercise 8 B|22 Videos

  • INTRODUCTION TO TRIGONOMETRY

    NAGEEN PRAKASHAN|Exercise Revision Exercise Long Answer Questions|5 Videos

  • CONSTRUCTIONS

    NAGEEN PRAKASHAN|Exercise PROBLEMS FROM NCERT/ EXEMPLAR|10 Videos

  • LINEAR EQUATIONS IN TWO VARIABLES

    NAGEEN PRAKASHAN|Exercise Revision Exercise Long Answer Questions|8 Videos

Similar Questions

Explore conceptually related problems

sqrt((1-cos^(2)theta)sec^(2)theta)=tan theta

Prove that sqrt(sec^(2)theta + cosec^(2)theta) = tantheta + cottheta .

sec^2theta/tantheta=?

Prove that sqrt((1-cos2 theta)/(1+cos2 theta))=tan theta where tan theta>0

Prove that sqrt((1-cos2 theta)/(1+cos2 theta))=tan theta where tan theta>0

If sin theta=(3)/(4), prove that sqrt((cos ec^(2)theta-cot^(2)theta)/(sec^(2)theta-1))=(sqrt(7))/(3)

Prove the following identities: sqrt(sec^(2)theta+cos ec^(2)theta)=tan theta+cot theta

Prove: cos ec theta sqrt(1-cos^(2)theta)=1

Prove: cosec theta sqrt(1-cos^(2) theta)=1

Prove that : sec^(2)theta - cos^(2) theta = sin^(2)theta(sec^(2)theta + 1)

NAGEEN PRAKASHAN-INTRODUCTION TO TRIGONOMETRY-Problems From NCERT/exemplar
  1. In DeltaA B C , right-angled at B, A B"\ "="\ "5"\ "c m and /A C B=30...

    Text Solution

    |

  2. In P Q R , right-angled at Q ,\ P Q=3c m and P R=6c m . Determine ...

    Text Solution

    |

  3. Prove that : sqrt((1-cos^(2)theta)sec^(2)theta)=tantheta

    Text Solution

    |

  4. Prove (tantheta+2)(2tantheta+1)=5tantheta+2sec^2theta.

    Text Solution

    |

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

    Text Solution

    |

  6. Prove the following identity: sec^4theta-sec^2theta=tan^4theta+tan^2th...

    Text Solution

    |

  7. Prove that : 1+(cot^(2)alpha)/(1+"cosec"alpha)="cesec"alpha

    Text Solution

    |

  8. Prove that : (sinalpha+cosalpha)(tanalpha+cotalpha)=secalpha+"cosecα...

    Text Solution

    |

  9. Prove that : (sintheta)/(1+costheta)+(1+costheta)/(sintheta)=2"cosec"t...

    Text Solution

    |

  10. If 2sin^(2)theta-cos^(2)theta=2, then find the value of theta.

    Text Solution

    |

  11. if tantheta+sectheta=l then prove that tantheta=(l^2+1)/(2l)

    Text Solution

    |

  12. If asintheta+bcostheta=c then prove that acostheta-bsintheta=sqrt(a^2+...

    Text Solution

    |

  13. If sintheta+costheta=pandsectheta+"cosec"theta=q then prove that q(p^(...

    Text Solution

    |

  14. Prove that : tantheta+tantheta+tan(90^(@)-theta)=sectheta*sec(90^(@)-t...

    Text Solution

    |

  15. Shown that : tan48^(@)tan23^(@)tan42^(@)tan67^(@)=1

    Text Solution

    |

  16. If tan A= cot B. prove that : A+B=90^(@)

    Text Solution

    |

  17. Express sin 67^(@)+cos75^(@) in terms of trigononmertic ratios of angl...

    Text Solution

    |

  18. If tan A=cot (A-18^(@)) where 2A is an acute angle , find the value of...

    Text Solution

    |

  19. If sec4A ="cosec"(A-20^@) where 4A is an acute angle , find the value ...

    Text Solution

    |

  20. The value of the expression cosec(75^(@)+theta)-sec(15^(@)-theta)-tan(...

    Text Solution

    |