Home
Class 12
MATHS
Let S(1) be the set of all those solutio...

Let `S_(1)` be the set of all those solution of the equation `(1+a) cos theta cos(2 theta-b)=(1+a cos 2 theta) cos (theta -b)`
which are independent of a and b and `S_(2)` be the set of all such solutions which are dependent on a and b. Then
The set `S_(1)` and `S_(2)` are

A

`|a/2 sin b| lt 1`

B

`|a/2 sin b| le 1`

C

`|a sin b| le 1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`sin (2 theta-b)=a sin b rArr |a sin b| le 1`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    CENGAGE ENGLISH|Exercise Exercises (Numerical value type)|21 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE ENGLISH|Exercise Archives ((JEE MAIN) Single correct Answer type)|2 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE ENGLISH|Exercise Exercises (Multiple correct type)|31 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise ARCHIVES INTEGER TYPE|1 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

Similar Questions

Explore conceptually related problems

Let S_1 be the set of all those solutions of the equation (1+a)costhetacos(2theta-b)=(1+a\ cos2theta)"cos"(theta-b) which are independent of a\ a n d\ b and S_2 be the set of all such solutions which are dependent on a\ a n d\ bdot The set S_1a n d\ S_2 are given by

The solution of the equation 1-"cos" theta = "sin" theta "sin" (theta)/(2) is

The number of solution of the equation sin theta cos theta cos 2 theta .cos 4theta =1/2 in the interval [0,pi]

(1+sin 2theta+cos 2theta)/(1+sin2 theta-cos 2 theta) =

Solution of the equation sin (sqrt(1+sin 2 theta))= sin theta + cos theta is (n in Z)

The number of solution the equation cos(theta).cos(pitheta)=1 has 0 (b) 2 (c) 4 (d) 2

The number of solution the equation cos(theta)cos(pitheta)=1 has 0 (b) 2 (c) 4 (d) 2

1 + (cos 2 theta + cos 6 theta)/(cos 4 theta) = (sin 3 theta)/(sin theta).

(1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=?

solve cos^(2)theta+cos theta=1

CENGAGE ENGLISH-TRIGONOMETRIC EQUATIONS-Exercises (Linked comprehension type)
  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) One of...

    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. For what values of 'b' does the equation ( b cos x)/( 2 cos 2x -1) =( ...

    Text Solution

    |

  20. For what values of 'b' does the equation ( b cos x)/( 2 cos 2x -1) =( ...

    Text Solution

    |