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
Condition that should be imposed on a and b such that `S_(2)` in non empty is

A

a. `|a/2 sin b| lt 1`

B

b. `|a/2 sin b| le 1`

C

c. `|a sin b| le 1`

D

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|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|4 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

Similar Questions

Explore conceptually related problems

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

Solve the equations: cos theta + cos 3theta = 2 cos 2theta

Show that (cosec theta -cot theta )^(2) =(1-cos theta )/( 1+cos theta )

Prove: (1 + cot^2 theta) (1 + cos theta)(1-cos theta) = 1

Solve the equations: sin 2theta - cos 2 theta - sin theta + cos theta = 0

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) 1 (c) 4 (d) 2

Prove that sin^(4) theta + cos^(4) theta = 1 - 2 sin^2 theta cos^(2) theta

Simplify (1-cos theta ) (1+cos theta ) (1+ cot ^(2) theta) .

CENGAGE-TRIGONOMETRIC EQUATIONS-Exercise (Comprehension)
  1. Consider the cubic equation x^(3)-(1+ cos theta+sin theta)x^(2)+(cos t...

    Text Solution

    |

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

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

    Text Solution

    |

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

    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

    |