Home
Class 10
MATHS
Prove the following identities: (cosA...

Prove the following identities: `(cosA)/(1-tanA)+(sinA)/(1-cotA)=cosA+sinA`

Text Solution

Verified by Experts

LHS=`cos A/(1-tanA)+sinA/(1-cotA)=cosA/(1-sinA/cosA)=sinA/(1-cosA/sinA)`
`cosA/((cosA-sinA)/cosA)+sinA((sinA-cosA)/sinA)`
`cos^2A/(cosA-sinA)=sin^2A/(sinA-cosA`
`(cos^2A-sin^2A)/(cosA-sinA)`
...
Promotional Banner

Topper's Solved these Questions

  • TRIANGLES

    RD SHARMA|Exercise All Questions|361 Videos

  • TRIGONOMETRIC RATIOS

    RD SHARMA|Exercise All Questions|249 Videos

Similar Questions

Explore conceptually related problems

Prove that : (cosA)/(1+tan A )-(sinA)/(1+cotA)= cosA - sin A

Consider the following 1. (cosA)/(1-tanA)+(sinA)/(1-cotA)=sinA+cosA 2. (1-sinA-cosA)^2=2(1-sinA)(1+cosA) Which of the above is/are identity/identities?

CosA/(1-SinA) + SinA/(1-CosA) + 1 =

Prove that (1+cosA)/(sinA) + (sinA)/(1+cosA) = 2/(sin A)

Prove that : (cosA)/(1+sin A) +(1+sinA)/(cosA)=2 sec A

(sinA)/(1+cosA)+(1+cosA)/sinA=2cosecA

Prove that: (1+cosA+sinA)/(1+cosA-sinA)=(1+sinA)/(cosA)

If cosecA=2 , then (1)/(tanA)+(sinA)/(1+cosA)=?

RD SHARMA-TRIGONOMETRIC IDENTITIES-All Questions
  1. Prove the following identities: (sin^3theta+cos^3theta)/(sintheta+c...

    Text Solution

    |

  2. Prove the following trigonometric identities: (tantheta+sintheta)...

    Text Solution

    |

  3. Prove the following identities: (cosA)/(1-tanA)+(sinA)/(1-cotA)=cos...

    Text Solution

    |

  4. Prove the following identities: (tanA)/(1-cotA)+(cotA)/(1-tanA)=1+t...

    Text Solution

    |

  5. Prove the following trigonometric identities: cottheta-tantheta=(2cos...

    Text Solution

    |

  6. Prove the following trigonometric identities: tantheta-cottheta=(2sin...

    Text Solution

    |

  7. Prove the following identities: tan^2theta+cot^2theta+2=sec^2thet...

    Text Solution

    |

  8. Prove the following identities: sqrt(sec^2theta+cos e c^2theta)=t...

    Text Solution

    |

  9. Prove the following identities: (sintheta+sectheta)^2+(costheta+cos e...

    Text Solution

    |

  10. Prove the following identities: (cos e ctheta-cottheta)^2=(1-costheta...

    Text Solution

    |

  11. Prove the following identities: sec^4A-sec^2A=tan^4A+tan^2A

    Text Solution

    |

  12. Prove the following identities: 2sec^2theta-sec^4theta-2cos e c^2th...

    Text Solution

    |

  13. Prove the following identities: (sintheta-sectheta)^2+(costheta-cos e...

    Text Solution

    |

  14. (sintheta)/(1+costheta)+(1+costheta)/(sintheta)=2cosectheta

    Text Solution

    |

  15. Prove the following identities: (tantheta-cottheta)/(sinthetacostheta...

    Text Solution

    |

  16. Prove the following identities: 1/(sectheta-tantheta)=sectheta+tanthe...

    Text Solution

    |

  17. Prove the following identities: (sec-tantheta)/(sectheta+tantheta)=1-...

    Text Solution

    |

  18. Prove the following identities: (tantheta+sectheta-1)/(tantheta-secth...

    Text Solution

    |

  19. Prove the following identities: (cotA+cos e cA-1)/(cotA-cos e cA+1)=(...

    Text Solution

    |

  20. Prove the following identities: (sintheta)/(cottheta+cos e ctheta)=2+...

    Text Solution

    |