Home
Class 10
MATHS
If x=asectheta+btantheta and y=atantheta...

If `x=asectheta+btantheta` and `y=atantheta+bsectheta` ,prove that : `x^2-y^2=a^2-b^2`.

Text Solution

Verified by Experts

`x=asecθ+btanθ`
`y=atanθ+bsecθ`
`x^2−y^2=a^2sec^2θ+b^2tan^2θ+2absecθtanθ−a^2tan^2θ−b^2sec^2θ−2absecθtanθ`
`=a^2(sec^2θ−tan^2θ)−b^2(sec^2θ−tan^2θ)`
...
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

If x=a sec theta+b tan theta and y=a tan theta+b sec theta then prove that x^(2)-y^(2)=a^(2)-b^(2)

If x=a cos theta-b sin theta and y=a sin theta+b cos theta then prove that :x^(2)+y^(2)=a^(2)+b^(2)

If x = a cos theta - b sin theta and y = a sin theta + b cos theta, prove that x^2 + y^2 = a^2 + b^2.

If x=a sin theta+b cos theta and y=a cos theta -b sin theta, " prove that " x^(2)+y^(2)=a^(2)+b^(2).

x=a sin theta , y=btantheta so prove that a^2/x^2-b^2/y^2=1

If a+btantheta=secthetaandb-atantheta=2sectheta, then: a^2+b^2=

If x=a sin theta and y=b tan theta, then prove that (a^(2))/(x^(2))-(b^(2))/(y^(2))=1

If x=a sec theta,y=b tan theta, then prove that (x^(2))/(a^(2))-(y^(2))/(b^(2))=1

If xcos theta- y sin theta =a, x sin theta + y cos theta = b , prove that: x^(2) + y^(2) = a^(2) + b^(2) .

If x = h+ asectheta and y=k + b"cosec"theta then

RD SHARMA-TRIGONOMETRIC IDENTITIES-All Questions
  1. Prove the trigonometric identities: If Tn=sin^ntheta+cos^ntheta, prove...

    Text Solution

    |

  2. Prove the trigonometric identities: (1+cotA+t a n A)(sin A-cos A)=(s ...

    Text Solution

    |

  3. If x=asectheta+btantheta and y=atantheta+bsectheta ,prove that : x^2...

    Text Solution

    |

  4. If x/a costheta+y/b sintheta=1 and x/a sintheta-y/bcostheta=1 Prove...

    Text Solution

    |

  5. If cos e ctheta-sintheta=a^3,sectheta-costheta=b^3, Prove that : a^2b...

    Text Solution

    |

  6. If acos^2theta+3acosthetas in^2theta=ma n das in^3theta+3acos^2thetas ...

    Text Solution

    |

  7. If 3sintheta+5costheta=5, then show that 5sintheta-3costheta=+-3.

    Text Solution

    |

  8. If acostheta+bsintheta=m and asintheta-bcostheta=n , Prove that a^2...

    Text Solution

    |

  9. If costheta+cos^2theta=1, Prove that: sin^(12)theta+3sin^(10)theta+3si...

    Text Solution

    |

  10. If cottheta=15/8, then Evaluate ((2+2sintheta)(1-sintheta))/((1+costhe...

    Text Solution

    |

  11. Prove the trigonometric identities: (tantheta)/(1-cottheta)+(cottheta)...

    Text Solution

    |

  12. If sintheta+costheta=x , Prove that : sin^6theta+cos^6theta=(4-3(x^2-1...

    Text Solution

    |

  13. Prove the following identities: ((1+sintheta)^2+(1-sintheta)^2)/(co...

    Text Solution

    |

  14. Prove that (1-sintheta+costheta)^2=2(1+costheta)(1-sintheta)

    Text Solution

    |

  15. Prove the following identities: (sinA+secA)^2+(cos"A"+"c o s e cA")^2=...

    Text Solution

    |

  16. Prove the following identities: (1+tanAtanB)^2+(tan"A"-tan"B")^2=sec^2...

    Text Solution

    |

  17. Prove the following identities: 2(sin^6theta+cos^6theta)-3(sin^4theta+...

    Text Solution

    |

  18. Prove the following identities: tan^2A-tan^2B=(cos^2B-cos^2A)/(cos^2Bc...

    Text Solution

    |

  19. If costheta+sintheta=sqrt(2)costheta, show that costheta-sintheta=sqrt...

    Text Solution

    |

  20. If tantheta+sintheta=m and tantheta-sintheta=n , then m^2-n^2=

    Text Solution

    |