Home
Class 12
MATHS
All the permissible value of b ,a=sin(2x...

All the permissible value of b ,a=sin(2x-b)if `a=0` and `x=S_(2)` is a subset of `(0, pi)` are given by

A

`b in (-n pi, 2npi), n in Z`

B

`b in (-n pi, 2pi - npi), n in Z`

C

`b in (-n pi, npi), n in Z`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`a=0 rArr sin (2 theta-b)=0`
`rArr 2 theta-b=n pi, n in Z`
`rArr theta=(n pi+b)/2, n in Z, S_(2)=(n pi +b)/2, n in Z`
`S_(2)` is subset of `(0, pi)`
`:. 0 lt (n pi +b)/2 lt pi, n in Z`
`:. 0 lt n pi +b lt 2pi rArr -n pi lt b lt -n pi +2pi`
`rArr b in (-n pi, 2pi-npi), n in Z`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercises (Matrix Match Type)|6 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise (Numerical)|21 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise (Multiple)|31 Videos

  • TRIGNOMETRIC RATIOS IDENTITIES AND TRIGNOMETRIC EQUATIONS

    CENGAGE|Exercise Question Bank|34 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

Similar Questions

Explore conceptually related problems

Let A denotes the set of values of x for which (x+2)/(x-4) le0 and B denotes the set of values of x for which x^2-ax-4 le 0. If B is the subset of A then a cannot take integral value (a) 0, (b) 1 (c) 2 (d) 3

The minimum value of a sec x+b cos ecx,0

If (sin alpha)x^(2)-2x+b>=2, for all real values of x<=1 and alpha in(0,(pi)/(2))uu(pi/2,pi), then possible real value of b is /are a2 b.3 c.4d.5

If all values of x in (a, b) satisfy the inequality tan x tan 3x lt -1, x in (0, (pi)/(2)) , then the maximum value of (b-a) is :

If all values of x in (a, b) satisfy the inequality tan x tan 3x lt -1, x in (0, (pi)/(2)) , then the maximum value (b, -a) is :

Let f(x) = {((1+|sin|)^(a/(|sin x|)),",",-(pi)/6 lt x lt 0),(b, ",",x = 0),(e^((tan 2x)/(tan3x)),",",0 lt x lt pi/6):} Then the value of a and b if f is continuous at x = 0, are respectively

CENGAGE-TRIGONOMETRIC EQUATIONS-Exercise (Comprehension)
  1. Cosider the cubic equation : x^3-(1+costheta+sintheta)x^2+(costhetasin...

    Text Solution

    |

  2. Consider the cubic equation x^3-(1+cos theta+sin theta)x^2+(cos theta ...

    Text Solution

    |

  3. Consider the cubic equation x^3-(1+cos theta+sin theta)x^2+(cos theta ...

    Text Solution

    |

  4. Consider the equation sec theta +cosec theta=a, theta in (0, 2pi) -{...

    Text Solution

    |

  5. Consider the equation sec theta +cosec theta=a, theta in (0, 2pi) -{...

    Text Solution

    |

  6. Consider the equation sec theta +cosec theta=a, theta in (0, 2pi) -{...

    Text Solution

    |

  7. Consider the system of equations sin x cos 2y=(a^(2)-1)^(2)+1, cos x...

    Text Solution

    |

  8. Consider the system of equations sin x cos 2y=(a^(2)-1)^(2)+1, cos x...

    Text Solution

    |

  9. Consider the system of equations sin x cos 2y=(a^(2)-1)^(2)+1, cos x...

    Text Solution

    |

  10. Cosider the equation int(0)^(x) (t^(2)-8t+13)dt= x sin (a//x) The nu...

    Text Solution

    |

  11. Cosider the equation int(0)^(x) (t^(2)-8t+13)dt= x sin (a//x) If x t...

    Text Solution

    |

  12. Cosider the equation int(0)^(x) (t^(2)-8t+13)dt= x sin (a//x) If x t...

    Text Solution

    |

  13. Consider the system of equations x cos^(3) y+3x cos y sin^(2) y=14 ...

    Text Solution

    |

  14. Consider the system of equations x cos^(3) y+3x cos y sin^(2) y=14 ...

    Text Solution

    |

  15. Consider the system of equations x cos^(3) y+3x cos y sin^(2) y=14 ...

    Text Solution

    |

  16. Let S(1) be the set of all those solution of the equation (1+a) cos th...

    Text Solution

    |

  17. Let S(1) be the set of all those solution of the equation (1+a) cos th...

    Text Solution

    |

  18. All the permissible value of b ,a=sin(2x-b)if a=0 and x=S(2) is a subs...

    Text Solution

    |

  19. Let (b cos x)/(2 cos 2x-1)=(b + sin x)/((cos^(2) x-3 sin^(2) x) tan x)...

    Text Solution

    |

  20. Let (b cos x)/(2 cos 2x-1)=(b + sin x)/((cos^(2) x-3 sin^(2) x) tan x)...

    Text Solution

    |