Home
Class 10
MATHS
Prove each of the following identities :...

Prove each of the following identities :
`(i) ("cosec"theta + cot theta )/("cosec"theta - cot theta ) = ("cosec" theta + cot theta)^(2) = 1+2cot^(2) theta + 2"cosec" theta cot theta `
` (ii) (sec theta + tan theta ) /( sec theta - tan theta) =(sec theta + tan theta )^(2) = 1+ 2tan^(2) theta + 2 sec theta tan theta `

Text Solution

Verified by Experts

(i) `LHS =(("cosec" theta+cot theta))/(("cosec" theta-cot theta))xx(("cosec" theta+cot theta))/(("cosec" theta+cot theta))=("cosec" theta+cot theta)^(2).`
And, `("cosec" theta+cot theta)^(2)="cosec"^(2)theta+cot^(2)theta+2 "cosec"theta cot theta`
`=(1+cot^(2)theta)+cot^(2)theta+2 "cosec"theta cot theta. `
(ii) `LHS=((sec theta +tan theta))/((sec theta -tan theta))xx((sec theta+tan theta))/((sec theta+tan theta)).`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC IDENTITIES

    RS AGGARWAL|Exercise Exercise 13B|15 Videos

  • TRIGONOMETRIC IDENTITIES

    RS AGGARWAL|Exercise Exercise 13C|40 Videos

  • TRIGONOMETRIC IDENTITIES

    RS AGGARWAL|Exercise Test Yourself|20 Videos

  • TRIANGLES

    RS AGGARWAL|Exercise Test Yourself|20 Videos

  • TRIGONOMETRIC RATIOS

    RS AGGARWAL|Exercise Exercise 10|35 Videos

Similar Questions

Explore conceptually related problems

Prove that: ("cosec" theta + cot theta)/("cosec" theta - cot theta) = ("cosec" theta + cot theta )^(2) = 1 + 2 cot^(2) theta + 2 "cosec" theta cot theta .

Prove each of the following identities : ((1+ tan^(2) theta) cot theta)/("cosec"^(2) theta ) = tan theta

Prove that (i) (1)/(("cosec" theta- cot theta ))=("cosec" theta + cot theta) (ii) ((sec theta - tan theta))/((sec theta + tan theta))=(1+ 2tan^(2) theta - 2 sec theta tan theta)

Prove each of the following identities : (tan theta)/((1-cot theta)) + (cot theta)/((1- tan theta)) = (1+ sec theta "cosec" theta)

Prove each of the following identities : (1+ tan theta + cot theta )( sin theta - cos theta ) =((sec theta)/("cosec"^(2) theta ) - ("cosec"theta)/(sec^(2)theta))

Prove that (i) (sin theta)/((1- cos theta))=("cosec" theta + cot theta) (ii) (1)/((sec theta - tan theta))=(sec theta + tan theta)

Prove each of the following identities : (i) (tan theta)/((sec theta -1)) + (tan theta)/((sec theta +1)) = 2 "cosec" theta (ii) (cot theta)/(("cosec" theta +1))+ (("cosec" theta +1))/(cot theta ) = 2 sec theta

Prove each of the following identities : (i) sec theta(1- sin theta)(sec theta + tan theta)=1 (ii) sin theta (1+ tan theta) + cos theta( 1+ cot theta)=( sec theta + "cosec" theta)

If (cosec theta - cot theta)=2 , the (cosec theta +cot theta) is equal to

RS AGGARWAL-TRIGONOMETRIC IDENTITIES-Exercise 13A
  1. Prove each of the following identities : (i) (tan theta)/((sec theta...

    Text Solution

    |

  2. Prove each of the following identities : (i) (sec theta -1)/(sec the...

    Text Solution

    |

  3. Prove each of the following identities : (i) sqrt((1+ sin theta)/(1-...

    Text Solution

    |

  4. Prove each of the following identities : (cos^(3) theta + sin^(3) th...

    Text Solution

    |

  5. Prove each of the following identities : (sin theta)/((cot theta + "...

    Text Solution

    |

  6. Prove each of the following identities : (i) (sin theta - cos theta)...

    Text Solution

    |

  7. Prove each of the following identities : (1+ cos theta - sin^(2) th...

    Text Solution

    |

  8. Prove each of the following identities : (i) ("cosec"theta + cot the...

    Text Solution

    |

  9. Prove each of the following identities : (i) (1+ cos theta + sin the...

    Text Solution

    |

  10. Prove that (sin theta)/(sec theta+tan theta-1)+cos theta/(cosec theta+...

    Text Solution

    |

  11. Prove each of the following identities : (sin theta + cos theta)/(s...

    Text Solution

    |

  12. (cos theta cosec theta-sin theta sec theta)/(cos theta+sin theta)=cose...

    Text Solution

    |

  13. Prove each of the following identities : (1+ tan theta + cot theta )...

    Text Solution

    |

  14. What will be the value of following identities : (cot^(2) theta (sec...

    Text Solution

    |

  15. Prove the following identity: (1/(sec^2theta-cos^2theta)+1/(cos e c^2t...

    Text Solution

    |

  16. Prove each of the following identities : ((sin A - sin B))/((cos A ...

    Text Solution

    |

  17. Prove: (tanA+tanB)/(cotA+cotB)=tanAtanB

    Text Solution

    |

  18. Show that none of the following is an identity: (i) cos^(2) theta +...

    Text Solution

    |

  19. Prove that: (sin theta - 2 sin^(3) theta) = (2cos^(3) theta - cos the...

    Text Solution

    |

  20. If 1+sin^2 theta= 3 sintheta cos theta, then prove that tan theta = 1 ...

    Text Solution

    |