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

Prove each of the following identities :
`( cos^(2) theta)/((1- tan theta)) + (sin^(3) theta)/((sin theta - cos theta)) = (1+ sin theta cos theta) `

Text Solution

Verified by Experts

Write ` tan theta = (sin theta )/(cos theta ) ` and simplify .
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 each of the following identities : (cos theta) /((1- tan theta)) - (sin^(2) theta)/((cos theta - sin theta)) = (cos theta + sin theta)

Prove the following identities: (cos^(2)theta)/(1-tan theta)+(sin^(3)theta)/(sin theta-cos theta)=1+sin theta cos theta

Prove each of the following identities : (sin theta)/((1+ cos theta)) + ((1+ cos theta))/(sin theta) = 2 "cosec" theta

Prove each of the following identities : (sin theta + cos theta)/(sin theta - cos theta) + (sin theta - cos theta)/(sin theta + cos theta) = (2) /((sin^(2) theta - cos^(2) theta)) = (2) /((2sin^(2) theta -1))

Prove each of the following identities : (i) (sin theta - cos theta)/(sin theta + cos theta) + ( sin theta+ cos theta)/(sin theta - cos theta) = (2)/((2 sin^(2) theta -1)) (ii) (sin theta + cos theta ) /(sin theta - cos theta) + ( sin theta - cos theta) /(sin theta + cos theta) = (2) /((1- 2 cos^(2) theta))

3. sin^(3)theta+cos^(3)theta=(sin theta+cos theta)(1-sin theta cos theta)

Prove each of the following identities : (cos^(3) theta + sin^(3) theta)/(cos theta + sin theta ) + (cos^(3) theta - sin^(3) theta)/(cos theta - sin theta ) = 2

(1 + cos theta + sin theta) / (1 + cos theta-sin theta) = (1 + sin theta) / (cos theta)

Prove that (cos theta)/((1-tan theta))-(sin^(2)theta)/((cos theta-sin theta))=(cos theta+sin theta)

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

RS AGGARWAL-TRIGONOMETRIC IDENTITIES-Exercise 13A
  1. Prove each of the following identities : (sin theta)/((1+ cos theta...

    Text Solution

    |

  2. Prove each of the following identities : (tan theta)/((1-cot theta)...

    Text Solution

    |

  3. Prove each of the following identities : ( cos^(2) theta)/((1- tan t...

    Text Solution

    |

  4. Prove each of the following identities : (cos theta) /((1- tan thet...

    Text Solution

    |

  5. Prove each of the following identities : (1+ tan^(2) theta)(1+ cot^(...

    Text Solution

    |

  6. Prove each of the following identities : (tan theta)/((1+ tan^(2) t...

    Text Solution

    |

  7. Prove each of the following identities : (i) sin^(6) theta + cos^(6...

    Text Solution

    |

  8. Prove each of the following identities : (i) (1- tan^(2) theta)/(1+ ...

    Text Solution

    |

  9. Prove each of the following identities : (i) (tan theta)/((sec theta...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |