Home
Class 10
MATHS
If cosectheta-sintheta=l, and sectheta-c...

If `cosectheta-sintheta=l`, and `sectheta-costheta=m` , show that `l^2m^2(l^2+m^2+3)=1` .

Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO TRIGONOMETRY

    MBD|Exercise EXERCISE|176 Videos

  • COORDINATE GEOMETRY

    MBD|Exercise EXERCISE|64 Videos

  • PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

    MBD|Exercise EXERCISE|183 Videos

Similar Questions

Explore conceptually related problems

If tantheta+sintheta=m,tantheta-sintheta=n , then show that m^2-n^2=4sqrt(mn) .

If cottheta+tantheta=m and sectheta-costheta=n then (i) sintheta costheta=-m (ii) sintheta tantheta=-n (iii) (m^2n)^(2/3)-(mn^2)^(2/3)=1 (iv) (m^2n)^(1/3)+(xy^2)^(1/3)=1

If costheta+sintheta=sqrt2costheta ,then show that costheta-sintheta=sqrt2 sintheta .

(sintheta+cosectheta)^2+(costheta+sectheta)^2=tan^2theta+cot^2+7 .

Prove tantheta/(sectheta-1)+(tantheta)/(sectheta+1)=2cosectheta .

Prove that (1+sintheta)/costheta+costheta/(1+sintheta)=2sectheta .

Prove that (sintheta)/(1+costheta)+(1+costheta)/sintheta=2cosectheta .

(m+2)sintheta+(2m-1)costheta=2m+1 then tan theta is

Prove that (cosectheta+cottheta)/(cosectheta-cottheta) =((1+costheta)/sintheta)^2 .

If l_(1), l_(2), l_(3) are respectively the perpendicular from the vertices of a triangle on the opposite side, then show that l_(1)l_(2) l_(3) =(a^(2)b ^(2) c^(2))/(8R^(3)).

MBD-INTRODUCTION TO TRIGONOMETRY-EXERCISE
  1. Prove that : (1+costheta-sin^2 theta)/(sintheta(1+costheta))=cottheta ...

    Text Solution

    |

  2. If sectheta+tantheta=p , prove that sintheta=(p^2-1)/(p^2+1) .

    Text Solution

    |

  3. If cosectheta-sintheta=l, and sectheta-costheta=m , show that l^2m^2(l...

    Text Solution

    |

  4. Prove that (cosectheta+cottheta)/(cosectheta-cottheta) =((1+costheta)/...

    Text Solution

    |

  5. Prove that (1+tan^2 theta)/(1+cot^2 theta)=((1-tantheta)/(1-cottheta)...

    Text Solution

    |

  6. Prove that cosA/(1-tanA)-(sin^2A)/(cosA-sinA)== sin A + cos A. .

    Text Solution

    |

  7. Prove that sec A (1 -sin A) (sec A + tan A) =1.

    Text Solution

    |

  8. Prove that (sec A + cos A) (sec A - cos A) = tan^2A+sin^2A .

    Text Solution

    |

  9. Prove that (1-tan^2theta)/(cot^2theta-1)=tan^2theta,thetane45^@ .

    Text Solution

    |

  10. Prove that (sin^2A)/(cos^2A)+(cos^2A)/(sin^2A)=1/(sin^2Acos^2A)-2 .

    Text Solution

    |

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

    Text Solution

    |

  12. Prove that ((1+sintheta)^2+(1-sintheta)^2)/(2cos^2theta)=(1+sin^2theta...

    Text Solution

    |

  13. Prove the following identities, where the angles involved are acute an...

    Text Solution

    |

  14. Prove that (1-costheta)/(1+costheta)=(cosectheta-cottheta)^2 .

    Text Solution

    |

  15. Prove that (1+sintheta)/costheta+costheta/(1+sintheta)=2sectheta .

    Text Solution

    |

  16. Prove that (1-sintheta)/(1+sintheta)=(sectheta-tantheta)^2 .

    Text Solution

    |

  17. Prove that (sintheta-2sin^3theta)/(2cos^3theta-costheta)=tantheta .

    Text Solution

    |

  18. tantheta-cottheta=(2sin^2theta-1)/(sinthetacostheta)=(1-2cos^2theta)/(...

    Text Solution

    |

  19. Prove that sintheta/(1-costheta)=cosectheta+cottheta .

    Text Solution

    |

  20. Prove that (1+tan^2theta)(1-sintheta)(1+sintheta)=1 .

    Text Solution

    |