Home
Class 12
MATHS
if cosalpha=1/2(x+1/x)andcosbeta=1/2(y+1...

if `cosalpha=1/2(x+1/x)andcosbeta=1/2(y+1/y),(xygt0),x,y,alpha,beta, inR`then

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(2)(x/y + y/x )`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS ENGLISH|Exercise Solved Examples : Single Option Correct Type Questions|2 Videos

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|10 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

  • VECTOR ALGEBRA

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|9 Videos

Similar Questions

Explore conceptually related problems

If cosalpha=1/2(x+1/x)a n dcosbeta=1/2(y+1/y),(x y >0); x , y ,alpha,beta in R then (a) sin(alpha+beta+gamma)=singammaAAgamma in R (b) cosalphacosbeta=1AAalpha,beta in R (c) (cosalpha+cosbeta)^2=4AAalpha,beta in R (d) sin(alpha+beta+gamma)=sinalpha+sinbeta+singamma AAa , b ,gamma in R

If cosalpha=1/2(x+1/x) cosbeta=1/2(y+1/y) then cos(alpha-beta) is equal to

If x/acosalpha+y/bsinalpha=1, x/acosbeta+y/bsinbeta=1 and (cos alpha cos beta)/a^2+(sin alpha sin beta)/b^2=0, then

If sinalpha-sinbeta=1/3andcosbeta-cosalpha=1/2, show that cot(alpha+beta)/2=2/3

If alpha=x_1,x_2,x_3 and beta=y_1,y_2,y_3 be two three digit numbers, then the number of pairs of alpha and beta that can be formed so that alpha can be subtracted from beta without borrowing.

If x cosalpha+y sinalpha=2a, x cos beta+y sinbeta=2aand 2sin""(alpha)/(2)sin""(beta)/(2)=1, then

The solution of the system of equations x+(cosalpha)y=1 and (cosalpha)x+4y=2 satisfy x ge(4)/(5) and yle(1)/(2) , then the value of alpha can lie in the inverval

The equations of the line through the point (alpha, beta, gamma) and equally inclined to the axes are (A) x-alpha=y-beta=z-gamma (B) (x-1)/alpha=(y-1)/beta=(z-1)/gamma (C) x/alpha=y/beta=z/gamma (D) none of these

If alpha&beta are the roots of the quadratic equation a x^2+b x+c=0 , then the quadratic equation, a x^2-b x(x-1)+c(x-1)^2=0 has roots: alpha/(1-alpha),beta/(1-beta) (b) alpha-1,beta-1 alpha/(alpha+1),beta/(beta+1) (d) (1-alpha)/alpha,(1-beta)/beta

If the line x/1=y/2=z/3 intersects the the line 3beta^(2)+3(1-2alpha)y+z=3-1/2{6alpha^(2)x+3(1-2beta)y+2z} then point (alpha,beta,1) lies on the plane

ARIHANT MATHS ENGLISH-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (Questions Asked In Previous 13 Years Exam)
  1. if cosalpha=1/2(x+1/x)andcosbeta=1/2(y+1/y),(xygt0),x,y,alpha,beta, in...

    Text Solution

    |

  2. Let alpha and beta be non-zero real numbers such that 2 ( cos beta -...

    Text Solution

    |

  3. Let -pi/6 < theta < -pi/12. Suppose alpha1 and beta1, are the roots of...

    Text Solution

    |

  4. The value of overset(13)underset(k=1)(sum) (1)/(sin((pi)/(4) + ((k-1)p...

    Text Solution

    |

  5. Let f:(-1,1)vecR be such that f(cos4theta)=2/(2-sec^2theta) for theta ...

    Text Solution

    |

  6. The number of all possible values of theta, where 0 lt theta lt pi, fo...

    Text Solution

    |

  7. For 0 lt theta lt pi/2 , the solution (s) of sum(m=1)^6cos e c(theta+(...

    Text Solution

    |

  8. If sin^ 4 x/2+cos^4 x/3 =1/5 then

    Text Solution

    |

  9. Let theta in (0,pi/4) and t1=(tan theta)^(tan theta), t2=(tan theta)^(...

    Text Solution

    |

  10. cos(alpha-beta)=1a n dcos(alpha+beta)=l/e , where alpha,betamu in [-pi...

    Text Solution

    |

  11. If 5 (tan ^(2) x - cos ^(2) x ) = 2 cos 2x +9, then the value of cos 4...

    Text Solution

    |

  12. Let F(k)(x)=1/k (sin^(k)x+cos^(k)x), where x in R and k ge 1, then fin...

    Text Solution

    |

  13. The expression (tanA)/(1-cotA)+(cotA)/(1-tanA) can be written as (1) s...

    Text Solution

    |

  14. If a Delta PQR " if" 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P =1 , ...

    Text Solution

    |

  15. If A = sin^2x + cos^4 x, then for all real x :

    Text Solution

    |

  16. Let cos(alpha+beta)""=4/5 and let sin (alpha+beta)""=5/(13) where 0lt=...

    Text Solution

    |

  17. If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma, then which...

    Text Solution

    |

  18. A triangular park is enclosed on two sides by a fence and on the third...

    Text Solution

    |

  19. If 0 lt x lt pi and cos x + sin x = 1/2, then tan x is

    Text Solution

    |

  20. In Delta PQR , /R=pi/4, tan(P/3), tan(Q/3) are the roots of the equati...

    Text Solution

    |