Home
Class 12
MATHS
Let 0 < θ1 < θ2 < θ3 < denote the po...

Let `0 < θ_1 < θ_2 < θ_3 <` denote the positive solution of the equation `3+3costheta=2sin^2theta` dot The value of `theta_3+theta_7` is

A

`6pi`

B

`7pi`

C

`8pi`

D

`4pi`

Text Solution

Verified by Experts

The correct Answer is:
A
`3+3 cos theta =2 -2 cos^(2) theta`
`rArr 2 cos^(2) theta+3 cos theta+1=0`
`rArr (2 cos theta+1) (cos theta+1) =0`
`:. Cos theta=-1 or cos theta=-1/2`
If `cos theta=-1` then `theta=pi, 3 pi, 5 pi, 7 pi, 9pi`, ...
If `cos theta=-1//2` then `theta=(2pi)/3, (4pi)/3, (8pi)/3, (10 pi)/3, (14 pi)/3, ...`
Solution in increasing order are
`(2pi)/3 lt pi lt (4pi)/3 lt (8 pi)/3 lt 3pi lt (10 pi)/3 lt (14 pi)/3 lt 5pi`, ...
`:. theta_(3)+theta_(7)=(4pi)/3+(14 pi)/3=6pi`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise (Multiple)|31 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Exercise 4.9|6 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 A = {0, 1, 2, 3, 4, 5}. Insert appropriate symbol inor!in in the blank spaces. 0 ______ A

Let A = {0,1,2,3}. Construct relation on A of the following type. not reflexive, not symmetric, not transitive

Let A = {0,1,2,3}. Construct relation on A of the following type. not reflexive, symmetric , not transitive

Let A = {0,1,2,3}. Construct relation on A of the following type. reflexive, not symmetric, not transitive

Let A = {0,1,2,3}. Construct relation on A of the following type. not reflexive, not symmetric, transitive

Let A = {0, 1, 2, 3, 4, 5}. Insert appropriate symbol inor!in in the blank spaces. 7 ______ A

Let A = {0, 1, 2, 3, 4, 5}. Insert appropriate symbol inor!in in the blank spaces. 6 _____ A

Let A = {0, 1, 2, 3, 4, 5}. Insert appropriate symbol inor!in in the blank spaces. 4 _______ A

Let A = {0, 1, 2, 3, 4, 5}. Insert appropriate symbol inor!in in the blank spaces. 3 ________ A

Let A = {0,1,2,3}. Construct relation on A of the following type. not reflexive, symmetric , transitive

CENGAGE-TRIGONOMETRIC EQUATIONS-Exercise (Single)
  1. Number of solutions of equation 2"sin" x/2 cos^(2) x-2 "sin" x/2 sin^(...

    Text Solution

    |

  2. Number of solutions of the equation 4(cos^(2) 2x+ cos 2 x +1)+tan x (t...

    Text Solution

    |

  3. Let 0 < θ1 < θ2 < θ3 < denote the positive solution of the equatio...

    Text Solution

    |

  4. Assume that theta is a rational multiple of pi such that cos theta is ...

    Text Solution

    |

  5. If x, y in [0, 2pi] and sin x + sin y=2, then the value of x+y is

    Text Solution

    |

  6. Number of roots of cos^2x+(sqrt(3)+1)/2sinx-(sqrt(3))/4-1=0 which lie ...

    Text Solution

    |

  7. The sum of all the solutions of cottheta=sin2theta(theta!=npi, n in t ...

    Text Solution

    |

  8. The number of solutions of 12 cos^(3) x-7 cos^(2) x+4 cos x=9 is

    Text Solution

    |

  9. Number of solutions of the equation sin x + cos x-2sqrt(2) sin x cos x...

    Text Solution

    |

  10. The general solution of (tan 5x-tan 4x)/(1+ tan 5 x tan 4x)=1 is

    Text Solution

    |

  11. If xsina+ysin2a+zsin3a=sin4a xsinb+ysin2b+zsin3b=sin4b xsinc+ysin2c+...

    Text Solution

    |

  12. The number of solutions of the equation sin 2 theta-2 cos theta +4 sin...

    Text Solution

    |

  13. The number of distinct real roots of the equation tan(2pix)/(x^2+x+1)=...

    Text Solution

    |

  14. The smallest positive value of x (in radians) satisfying the equation ...

    Text Solution

    |

  15. The number of solution of sin^(4)x-cos^(2) x sin x+2 sin^(2)x+sin x=0 ...

    Text Solution

    |

  16. The range of 'y, such that the equation in x, y + cos x = sin x has a ...

    Text Solution

    |

  17. Solution of the equation sin (sqrt(1+sin 2 theta))= sin theta + cos th...

    Text Solution

    |

  18. One of the general solutions of sqrt(3)costheta-3s intheta=4sin2thetac...

    Text Solution

    |

  19. The general solution of the equation 8 cos x cos 2x cos 4x = sin 6x//s...

    Text Solution

    |

  20. (sin^(3) theta-cos^(3) theta)/(sin theta - cos theta)- (cos theta)/sqr...

    Text Solution

    |