Home
Class 12
MATHS
If X=x cos theta-y sin theta, Y=x sin t...

If `X=x cos theta-y sin theta, Y=x sin theta+y cos theta and X^(2)+4XY+Y^(2)=Ax^(2)+By^(2), 0 le theta le pi//2`, then :
(where A and B are constants)

A

`theta = (pi)/(6), A = 3, B = 1`

B

`theta = (pi)/(4), A = 3, B =1`

C

`A =3, B=-1, theta = (pi)/(4)`

D

`A = -3, B = 1, theta = (pi)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|66 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|20 Videos

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 Videos

Similar Questions

Explore conceptually related problems

If x = X cos theta- Y sin theta, y = X sin theta + Y cos theta and x^2 + 4 x y + y^2 = A X^2 + B Y^2 0 <= theta <= pi/2, then

If x/a cos theta + y/b sin theta = 1 , x/a sin theta - y/b cos theta = 1 then x^2/a^2 + y^2/b^2 =

If x =2 cos theta - cos 2 theta y = 2 sin theta - sin 2 theta Find (d^(2)y)/(dx^(2)) at theta = pi/2

If x +y= 3-cos4theta and x-y=4sin2theta then

Let x= cos theta and y = sin theta for any real value theta . Then x^(2)+y^(2)=

If x = 3 cos theta - 2 cos^3 theta,y = 3 sin theta - 2 sin^3 theta , then dy/dx is

Solve cos theta * cos 2 theta * cos 3 theta = (1)/( 4), 0 le theta le pi

if x = "cos" theta - "cos" 2 theta, y = "sin" theta - "sin" 2 theta , then dy/dx is

If x sin^3 theta+ y cos^3 theta = sin theta cos theta and x sin theta = y cos theta, Find the value of x^2 + y^2.

If x= a sin 2theta (1+ cos 2theta) , y= b cos 2theta(1- cos 2theta) , then (dy)/(dx) =

OBJECTIVE RD SHARMA ENGLISH-TRIGONOMETRIC EQUATIONS AND INEQUATIONS-Chapter Test
  1. The general solution of the trigonometic equation "sin"x + "cos"x = 1...

    Text Solution

    |

  2. The general solution of the equation sin^2thetasectheta+sqrt3 tantheta...

    Text Solution

    |

  3. If X=x cos theta-y sin theta, Y=x sin theta+y cos theta and X^(2)+4XY...

    Text Solution

    |

  4. The equation 3^(sin2x+2cos^(2)x)+3^(1-sin2x+2sin^(2)x) = 28 is satisfi...

    Text Solution

    |

  5. The value of x , 0 le x le (pi)/2 which satisfy the equation 81^( si...

    Text Solution

    |

  6. The smallest positive values of x and y which satisfy "tan" (x-y) =1, ...

    Text Solution

    |

  7. The solution set of the inequality "cos"^(2) theta lt (1)/(2), is

    Text Solution

    |

  8. The equation sin^4x+cos^4x+sin2x+alpha=0 is solvable for -5/2lt=alphal...

    Text Solution

    |

  9. The equation "sin"^(4) x -2 "cos"^(2) x + a^(2) =0 is solvable if

    Text Solution

    |

  10. The number of points in interval [ - (pi)/(2) , (pi)/(2)], where the ...

    Text Solution

    |

  11. If 1/6 sinx, cosx, tan x are in G.P. then x=,

    Text Solution

    |

  12. Find the minimum value of 2^("sin" x) + 2^("cos" x)

    Text Solution

    |

  13. From the identity "sin" 3x = 3 "sin"x - 4"sin"^(3)x it follows that if...

    Text Solution

    |

  14. Find the most general solution of 2^1|cosx|+cos^2x+|cosx|^(3+oo)=4

    Text Solution

    |

  15. Let alpha, beta be any two positive values of x for which 2"cos"x, |"c...

    Text Solution

    |

  16. If max {5 sin theta + 3 sin ( theta - alpha )}=7 , then the set of pos...

    Text Solution

    |

  17. The most general value of theta for which "sin" theta-"cos" theta = ...

    Text Solution

    |

  18. The number of points of intersection of two curves y=2sinxa n dy=5x^2+...

    Text Solution

    |

  19. Let 2 sin^(2)x + 3 sin x -2 gt 0 and x^(2)-x -2 lt 0 ( x is measured ...

    Text Solution

    |

  20. The largest positive solution of 1+"sin"^(4) x = "cos"^(2) 3x " in " [...

    Text Solution

    |