Home
Class 10
MATHS
If x=a sin theta and y=b tan theta, the...

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

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRIGONOMETRIC IDENTITIES

    CALCUTTA BOOK HOUSE|Exercise EXERCISE|66 Videos

  • THEOREMS RELATED TO TANGENT IN A CIRCLE

    CALCUTTA BOOK HOUSE|Exercise EXERCISE 4.2|23 Videos

  • TRIGONOMETRIC RATIOS OF COMPLEMENTARY ANGLES

    CALCUTTA BOOK HOUSE|Exercise EXERCISE|28 Videos

Similar Questions

Explore conceptually related problems

If x=a sec theta cosphi, y = b sec theta sin phi and z=c tan theta , then prove that (x^(2))/(a^(2))+(y^(2))/(b^(2))-(z^(2))/(c^(2))=1.

If k tan theta=tan k theta , then prove that (sin^(2)k theta)/(sin^(2)theta)=(k^(2))/((k^(2)-1)sin^(2)theta+1).

If x_(1) and y_(1) be the intercepts on the x and y-axis respectively of tangent to the curve x= a cos^(3) theta, y = b sin ^(3) theta at any point theta , on the then priove that, (x_(1)^(2))/(a^(2))+(y_(1)^(2))/(b^(1))=1

If x=r cos theta cos phi, y=r cos theta sin phi, z=r sin theta , then prove that x^(2)+y^(2)+z^(2)=r^(2).

If sin theta+cos theta=a,tan theta+cot theta=b, show that (a^(2)-1)/(2)=(1)/(b)

If:x/a costheta+y/b sin theta=1 and x/a sin theta-y/b cos theta=1, Prove that : (x^2)/(a^2)+(y^2)/(b^2)=2

If x=cosec theta-sin theta and y=cosec^(n)theta-sin^(n) theta , prove that, (x^(2)+4)((dy)/(dx))^(2)=n^(2)(y^(2)+4) .

If x= cosec theta -sin theta and y=sec theta-cos theta, then show that x^(2//3)+y^(2//3)=(xy)^(-2//3)

If sec theta+tan theta = x , prove that sin theta= (x^2-1)/(x^2+1)

CALCUTTA BOOK HOUSE-TRIGONOMETRIC RATIOS AND TRIGONOMETRIC IDENTITIES -EXERCISE
  1. If x=a sin theta and y=b tan theta, then prove that (a^(2))/(x^(2))-(...

    Text Solution

    |

  2. If tan theta=(p)/(q), what is the value of (p sec theta-q " cosec" t...

    Text Solution

    |

  3. In DeltaABC, right angled at B, AB:AC=1:sqrt(2), then (2 tan A)/(1-ta...

    Text Solution

    |

  4. (sin30^(@)cos45^(@))/(tan 60^(@)) is equal to

    Text Solution

    |

  5. In DeltaABC, If angleC=90^(@), angleA=60^(@) and AB=40 cm, then AC is ...

    Text Solution

    |

  6. Write true of false : cot theta=(cos theta)/(sin theta)

    Text Solution

    |

  7. Write true of false : sin theta is a product of sin and theta.

    Text Solution

    |

  8. Fill in the blanks : The trigonometric ratio cos theta= ul(" ...

    Text Solution

    |

  9. Fill in the blanks : The value of sin theta can never be greate th...

    Text Solution

    |

  10. Fill in the blanks : The value of cot 0^(@) is not .

    Text Solution

    |

  11. Find the value of cos(-1170^(@)).

    Text Solution

    |

  12. Calculate the value of sec(-1680^(@)) sin 330^(@).

    Text Solution

    |

  13. Simplify : sin 300^(@) cos 390^(@) tan (-855^(@))+cos(-120^(@))* sin ...

    Text Solution

    |

  14. Prove that tan 225^(@) cot 405^(@)+tan 765^(@) cot 675^(@)=0.

    Text Solution

    |

  15. Evalute : "sin"^(2)(pi)/(4) + "cos"^(2) (3pi)/(4)+"cos"^(2)(5pi)/(4)...

    Text Solution

    |

  16. Prove that "tan"(pi)/(12) "tan"(pi)/(16) "tan"(5pi)/(12)"tan"(7pi)/(1...

    Text Solution

    |

  17. If tan 35^(@)=x, then prove that (tan 145^(@)- tan 125^(@))/(1+tan14...

    Text Solution

    |

  18. Find the value of sin^(3)60^(@) cot 30^(@)-2 sec^(2) 45^(@)+3 cos60^(@...

    Text Solution

    |

  19. If (cos theta)/(1-sin theta)-(costheta)/(1+sin theta)=2, then find the...

    Text Solution

    |

  20. If (cos x)/(cosy)=n and (sinx)/(siny)=m, what is the value of (m^(2)...

    Text Solution

    |

  21. If x cos 60^(@)+y cos0^(@)=3 and 4x sin 30^(@) -y cot 45^(@)=2, then ...

    Text Solution

    |