Home
Class 10
MATHS
Prove the following identity: sec^4theta...

Prove the following identity: `sec^4theta-sec^2theta=tan^4theta+tan^2theta`

Text Solution

Verified by Experts

LHS `=tan^(4)theta + tan^(2)theta = tan^(2)theta(tan^(2)+1)`
`=tan^(2)theta.sec^(2)theta.` `[therefore sec^(2)theta= tan^(2)theta+1]`
`=(sec^(2)-1).sec^(2)theta` `[therefore tan^(2)theta= sec^(2)theta-1]`
`=sec^(4)theta- sec^(2)theta=`RHS
Promotional Banner

Topper's Solved these Questions

  • COORDINATE GEOMETRY

    NCERT EXEMPLAR|Exercise Coordinate Geometry|58 Videos

  • PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

    NCERT EXEMPLAR|Exercise Exercise 3.3 Short Answer Type Questions|2 Videos

Similar Questions

Explore conceptually related problems

Prove the following identity: sec^(4)theta-sec^(2)theta=tan^(4)theta+tan^(2)theta

Prove the identity sec^(4)theta-sec^(2)theta=tan^(4)theta+tan^(2)theta

Prove the following identities: 2sec^(2)theta-sec^(4)theta-2cos ec^(2)theta+cos ec^(4)theta=cot^(4)theta-tan^(4)theta

Prove the following identities: 2sec^(2)theta-sec^(4)theta-2cos ec^(2)theta=cot^(4)theta-tan^(4)theta

Prove the following identity: (tan theta+sec theta-1)/(tan theta-sec theta+1)=(1+s int n eta)/(cos theta)

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

Prove the following Identities (sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)

Prove the following identity: (1+cot theta-cos ec theta)(1+tan theta+sec theta)=2

Prove the following identities: (sec-tan theta)/(sec theta+tan theta)=1-2sec theta tan theta+2tan^(2)theta

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

NCERT EXEMPLAR-INTRODUCTION TO TRIGoNOMETRY AND ITS APPLICATIONS-Introduction To Trigonometry And Its Applications
  1. Evaluate : (cos^2(45 + theta) + cos^2(45 - theta))/(tan(60^@ + theta)...

    Text Solution

    |

  2. An observer, 1.5 m tall, is 20.5 m away from a tower 22 m high. Determ...

    Text Solution

    |

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

    Text Solution

    |

  4. If cosectheta + cottheta=p, then cos theta=

    Text Solution

    |

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

    Text Solution

    |

  6. The angle of elevation of the top of a tower from a certain point is 3...

    Text Solution

    |

  7. If 1+sin^(2)theta = 3sinthetacostheta, then prove that tantheta=1 or 1...

    Text Solution

    |

  8. If sintheta + 2 costheta=1,then 2sintheta-costheta=

    Text Solution

    |

  9. The angle of elevation of the top of a tower from two distinct points ...

    Text Solution

    |

  10. The shadow of a tower standing on a level ground is found to be 40 m ...

    Text Solution

    |

  11. A vertical tower Stands on a horizontal plane and is surmounted by a v...

    Text Solution

    |

  12. if tantheta+sectheta=l then tantheta=

    Text Solution

    |

  13. If sin theta+ cos theta = p and sec theta + cosec theta = q; show that...

    Text Solution

    |

  14. If a sintheta + bcos theta = c, then prove that a costheta -b sintheta...

    Text Solution

    |

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

    Text Solution

    |

  16. The angle of elevation of the top of a tower 30 m high from the foot ...

    Text Solution

    |

  17. From the top of a tower h m high, angles of depression of two objects,...

    Text Solution

    |

  18. A ladder rests against a vertical wall at inclination alpha to the hor...

    Text Solution

    |

  19. The angle of elevation of the top of a vertical tower from a point on ...

    Text Solution

    |

  20. From a window ( h meter above ground) the angle of elevation of other ...

    Text Solution

    |