Home
Class 11
MATHS
If alpha=3sin^-1(6/(11)) and beta=3cos^-...

If `alpha=3sin^-1(6/(11))` and `beta=3cos^-1(4/9)`, where the inverse trigonometric functions take only the principal values, then the correct option(s) is(are)

A

`cosbeta gt 0`

B

`sinbeta lt 0`

C

`cos(alpha +beta) gt 0`

D

`cosalpha lt 0`

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|21 Videos
  • TRIGONOMETRIC FUNCTIONS

    PATHFINDER|Exercise QUESTION BANK|68 Videos

Similar Questions

Explore conceptually related problems

If alpha = 3 sin ^(-1) ""((6)/(11) )and beta =3 cos ^(-1)""((4)/(9)) , where the inverse trigonometric function take only the priencipal values , then the correct option (s) is are -

The principal value of cos^(-1)("cos"(11pi)/(6)) is -

Find the principal values of sin^(-1)sin ((3pi)/(4))

The principal values of cos^(-1)(-sin((7pi)/(6))) is

The principal value of sin^(-1)sin((3pi)/4) is

If we consider only the principal values of the inverse trigonometric functions , then the value of tan(cos^-1 (1/(5sqrt2)) -sin^-1 (4/sqrt(17))) is (a) sqrt(29)/3 (b) 29/3 (c) sqrt3/29 (d) 3/29

If alpha=int_(0)^(1)(e^(9x+3tan^(-1)x)((12+9x^(2))/(1+x^(2)))dx where tan^(-1)x takes only principal values, then the value of (log_(e)|1+alpha|-(3pi)/(4)) is-

The principal value of sin^-1 (-sqrt3/2)+cos^-1 cos((7pi)/6) is

If alpha=int_0^1(e^(9x+3tan^-1x))((12+9x^2)/(1+x^2))dx where tan^-1x takes only principal value, then the value of (log_eabs(1+alpha)-(3pi)/4) is

Express the following as sum or difference of two trigonometric functions:- 2 sin 11x cos 9x

PATHFINDER-TRIGONOMETRIC EQUATION AND INVERSE-QUESTION BANK
  1. Solve: 2cos^2x+5cosx+2 ge 0

    Text Solution

    |

  2. Find the points of intersection of the curves y=cosx and y=sin3x if -p...

    Text Solution

    |

  3. Solve for x and y : 2^(1/cos^2x)sqrt(y^2-y+1//2) le 1

    Text Solution

    |

  4. Find the value of tan^-1(1/2tan2A)+tan^-1(cotA)+tan^-1(cot^3A), for 0 ...

    Text Solution

    |

  5. Solve: sin^-1x+sin^-1(1-x)=cos^-1x

    Text Solution

    |

  6. Prove that: tan^-1((c1x-y)/(c1y+x))+tan^-1((c2-c1)/(1+c2c1))+tan^-1((c...

    Text Solution

    |

  7. The value of 'a' for which ax^2 + sin^-1 (x^2 - 2x + 2) + cos^-1 (x^2 ...

    Text Solution

    |

  8. The number of distinct solutions of the equation 5/4cos^2 2x+cos^4x+si...

    Text Solution

    |

  9. If alpha=3sin^-1(6/(11)) and beta=3cos^-1(4/9), where the inverse trig...

    Text Solution

    |

  10. Let, tan^-1y=tan^-1x+tan^-1((2x)/(1-x^2)), where absx lt 1/sqrt3. Then...

    Text Solution

    |

  11. The number of real solutions of the equation (sinx-x)(cosx-x^2)=0 is

    Text Solution

    |

  12. The values of 2cot^-1 (1/2)-cot^-1 (4/3) is

    Text Solution

    |

  13. The number of distinct roots of abs((sinx, cosx, cosx),(cosx, sinx, co...

    Text Solution

    |

  14. The trigonometric equation sin^-1x=2sin^-1 2a has a real solution if

    Text Solution

    |

  15. Let alpha, beta be two distinct roots of acostheta+bsintheta=c, where ...

    Text Solution

    |

  16. If sin^-1(x/(13))+cosec^-1((13)/(12))=pi/2, then the value of x is

    Text Solution

    |

  17. The value of cot(sum(n=1)^(23)cot^-1(1+sum(k=1)^n2k)) is

    Text Solution

    |

  18. If sin^-1x+sin^-1y+sin^-1z=(3pi)/2, then the value of x^9+y^9+z^9-1/(x...

    Text Solution

    |

  19. Number of solutions of the equation tanx+secx=2cosx, x in [0, pi] is

    Text Solution

    |

  20. The solutions set of inequation cos^-1x lt sin^-1x is

    Text Solution

    |