Home
Class 12
MATHS
The equation sin^2theta=(x^2+y^2)/(2x y)...

The equation `sin^2theta=(x^2+y^2)/(2x y),x , y!=0` is possible if

A

x = y

B

x = - y

C

2x = y

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Now, `sin^2theta=(x^2+y^2)/(2xy)`
`:. ` x,y have same sign
Now `(x^2+y^2)/(2xy)=1/2[(sqrt(x/y)-sqrt(y/x))^2+2]ge1`
But `sinthetale1," Therefore", (x^2+y^2)/(2xy)=1`
`rArrx=y`.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|17 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|11 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 2.6|9 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Archives (Matrix Match Type)|1 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Matrix Match Type|1 Videos

Similar Questions

Explore conceptually related problems

The equation sec ^2 theta = ( 4xy )/( ( x+y)^2) is possible for x,y, in R only if

sin theta = ( x + Y)/( 2 sqrt(xy)) is possible

The number of ordered pair (x, y) satisfying the equation sin^(2) (x+y)+cos^(2) (x-y)=1 which lie on the circle x^(2)+y^(2)=pi^(2) is _________.

The solution of the equation (x^2y+x^2)dx+y^2(x-1)dy=0 is given by

The equation x^(2)y^(2)-9y^(2)-6x^(2)y+54y=0 represents

If the conics whose equations are S_1:(sin^2theta)x^2+(2htantheta)x y+(cos^2theta)y^2+32 x+16 y+19=0 S_2:(cos^2theta)x^2-(2h^(prime)cottheta)x y+(sin^2theta)y^2+16 x+32 y+19=0 intersect at four concyclic points, where theta[0,pi/2], then the correct statement(s) can be (a) h+h^(prime)=0 (b) h-h^(prime)=0 (c) theta=pi/4 (d) none of these

The equation of the tangent tothe curve y={x^2 sin(1/x),x!=0 and 0, x=0 at the origin is

Suppose that for some angles xa n dy , the equations sin^2x+cos^2y=(3a)/2a n dcos^2x+sin^2y=(a^2)/2 hold simultaneously. the possible value of a is ___________

Identify the type of conic section for each of the equations 1. 2x^(2) -y^(2) = 7 2. 3x^(2) +3 y^(2) -4x + 3y + 10 =0 3. 3x^(2) + 2y^(2) = 14 4. x^(2) + y^(2) + x-y=0 5. 11x^(2) -25y^(2) -44x + 50y - 256 =0 6. y^(2) + 4x + 3y + 4=0

Find the equation of the radical axis of x^2 + y^2 – 2x – 4y – 1= 0, x^2 + y^2 – 4x – 6y + 5 = 0 .

CENGAGE-TRIGONOMETRIC FUNCTIONS -Exercise (Single)
  1. Given that the side length of a rhombus is the geometric mean of the ...

    Text Solution

    |

  2. Which of the following is correct?

    Text Solution

    |

  3. The equation sin^2theta=(x^2+y^2)/(2x y),x , y!=0 is possible if

    Text Solution

    |

  4. If sin^2theta=(x^2+y^2=1)/(2x) , then x must be -3 (b) -2 (c) 1 (d)...

    Text Solution

    |

  5. The equation sec ^2 theta = ( 4xy )/( ( x+y)^2) is possible for x...

    Text Solution

    |

  6. If sintheta1+sintheta2+sintheta3, then costheta1+costheta2+costheta3 i...

    Text Solution

    |

  7. If sinx+siny+sinz+sinw=-4" then the value of "sin^400x+sin^300y+sin^20...

    Text Solution

    |

  8. about to only mathematics

    Text Solution

    |

  9. If 1+sinx+sin^2x+sin^3x+oo is equal to 4+2sqrt(3),0<x<pi, then x is eq...

    Text Solution

    |

  10. The value of expression (2sin^2 91^0-1)(2sin^2 92^0-1)(2sin^2 180^0-1)...

    Text Solution

    |

  11. If sinA=sin^2B and 2cos^2A=3cos^2B then the triangle ABC is

    Text Solution

    |

  12. If sintheta+costheta=1/5a n d0lt=theta<pi, then tantheta is -4/3 (b) ...

    Text Solution

    |

  13. If pi,t h e nsqrt((1-cosalpha)/(1+cosalpha))+sqrt((1+cosalpha)/(1-cosa...

    Text Solution

    |

  14. IF tan alpha = ( sin alpha - cos alpha )/( sin alpha + cos alpha)...

    Text Solution

    |

  15. The least value of 2sin^2theta+3cos^2theta is 1 (b) 2 (c) 3 (d) ...

    Text Solution

    |

  16. The greatest value of sin^4theta+cos^4thetai s 1/2 (b) 1 (c) 2 (d...

    Text Solution

    |

  17. If f(x)=sin^6x+cos^6x , then range of f(x) is [1/4,1] (b) [1/4,3/4] ...

    Text Solution

    |

  18. The minimum value of atan^2x+bcot^2x equals the maximum value of asin^...

    Text Solution

    |

  19. Range of f(theta)=cos^2theta(cos^2theta+1)+2sin^2theta is [3/4,1] (b)...

    Text Solution

    |

  20. If 0<theta<pi, then minimum value of 3sintheta+cos e c^3theta is 4 (b)...

    Text Solution

    |