Home
Class 11
MATHS
If cosalpha=1/2(x+1/x)a n dcosbeta=1/2(y...

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`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

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

If cosalpha+cosbeta=0=sinalpha+sinbeta , then prove that cos2alpha +cos2beta=-2cos(alpha +beta) .

If alpha,beta,gamma, in (0,pi/2) , then prove that (s i(alpha+beta+gamma))/(sinalpha+sinbeta+singamma)<1

If "cot"(alpha+beta)=0, then "sin"(alpha+2beta) can be (a) -sinalpha (b) sinbeta (c) cosalpha (d) cosbeta

If sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>sin(alpha+beta) =

Evaluate |(cosalphacosbeta,cosalpha sinbeta , - sin alpha),(-sin beta,cosbeta,0),(sinalphacosbeta,sinalpha sinbeta,cosalpha)|

If 2 sin alphacos beta sin gamma=sinbeta sin(alpha+gamma),then tan alpha,tan beta and gamma are in

If cos(alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)=-3/2 , prove that cosalpha+cosbeta+cosgamma=sinalpha+sinbeta+singamma=0

sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>sin(alpha+beta)

If the lines x(sinalpha+sinbeta)-ysin(alpha-beta)=3 and x(cosalpha+cosbeta)+ycos(alpha-beta)=5 are perpendicular then sin2alpha+sin2beta is equal to:

CENGAGE ENGLISH-TRIGONOMETRIC FUNCTIONS-All Questions
  1. The equation sin^4x+cos^4x+sin2x+alpha=0 is solvable for -5/2lt=alphal...

    Text Solution

    |

  2. In triangle A B C , if r1=2r2=3r3, then a : b is equal to 5/4 (b) 4/5...

    Text Solution

    |

  3. If cosalpha=1/2(x+1/x)a n dcosbeta=1/2(y+1/y),(x y >0); x , y ,alpha,b...

    Text Solution

    |

  4. In triangle A B C ,(sinA+sinB+sinC)/(sinA+sinB-sinC) is equal to

    Text Solution

    |

  5. The radii r1,r2,r3 of enscribed circles of triangle ABC are in HP . If...

    Text Solution

    |

  6. Let alphaa n dbeta be any two positive values of x for which 2cosx ,|c...

    Text Solution

    |

  7. If (y+3)/(2y+5)=sin^2x+2cosx+1, then the value of y lies in the interv...

    Text Solution

    |

  8. If alpha+beta+gamma=2pi, then (a) tan(alpha/2)+tan(beta/2)+tan(gamma...

    Text Solution

    |

  9. The total number of solution of |cotx|=cotx+1/(sinx),x in [0,3pi] , is...

    Text Solution

    |

  10. The value of f(alpha)=sqrt(cos e c^2alpha-2cotalpha)+sqrt(cos e c^2alp...

    Text Solution

    |

  11. If I is the incenter of a triangle ABC, then the ratio I A : I B : I C...

    Text Solution

    |

  12. If asinx+bcos(x+theta)+bcos(x-theta)=d , then the minimum value of |c...

    Text Solution

    |

  13. The number of solution the equation cos(theta).cos(pitheta)=1 has 0 ...

    Text Solution

    |

  14. Let the incircle with center I of A B C touch sides BC, CA and AB at ...

    Text Solution

    |

  15. If x=secvarphi-tanvarphia n dy=cos e cvarphi+cotvarphi, then x=(y+1)/(...

    Text Solution

    |

  16. Prove that 5costheta+3cos(theta+pi/3)+3 lies between -4a n d10.

    Text Solution

    |

  17. The general solution of cosxcos6x=-1 is (a) x=(2n+1)pi,n in Z (b) x=...

    Text Solution

    |

  18. In an acute angled triangle A B C , a semicircle with radius ra is con...

    Text Solution

    |

  19. If f(x)=sin^6x+cos^6x , then range of f(x) is

    Text Solution

    |

  20. Which of the following number(s) is/are rational? (a)sin15^0 (b) co...

    Text Solution

    |