Home
Class 12
MATHS
The number of solutions of 12 cos^(3) x-...

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

A

0

B

2

C

infinite

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
The given equation is
`(cos x-1) (12 cos^(2) x+5 cos x+9)=0`
`rArr cos x=1` only as the other factor gives imaginary roots
`rArr x= 2n pi, n in Z`
Hence, it has infinite solutions as `n in Z`.
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

The number of solutions of 12cos^3x-7cos^2x+4cosx=9 is 0 (b) 2 (c) infinite (d) none of these

The number of solution (s) of cos sqrt3 x+cos sqrt5 x=2 is

The number of solutions of [sin x+ cos x]=3+ [- sin x]+[-cos x] (where [.] denotes the greatest integer function), x in [0, 2pi] , is

cos 3 x cos 2 x

The number of solution of sin x+sin 2x+sin 3x =cos x +cos 2x+cos 3x, 0 le x le 2pi , is

The total number of solution of the equation sin^4 x +cos^4 x = sin x cos x in [0,2pi] is :

The number of solution of the equation |cos x|=cos x-2 sin x "in"[0,6 pi] is

The number of solutions of the equation 16(sin^(5)x +cos^(5)x)=11(sin x + cos x) in the interval [0,2pi] is

Find the number of solutions to cos x = (x)/(10), x gt 0.

The number of solutions of the equation cos^2(x+pi/6)+cos^2x-2cos(x+pi/6)dotcospi/6=sin^2pi/6 in interval ((-pi)/2,pi/2) is_________

CENGAGE-TRIGONOMETRIC EQUATIONS-Exercise (Single)
  1. Number of roots of cos^2x+(sqrt(3)+1)/2sinx-(sqrt(3))/4-1=0 which lie ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. For 0ltx ,yltpi,the number of ordered pairs (x, y) satisfying system e...

    Text Solution

    |

  17. The least positive solution of cot(pi/(3sqrt3) sin2x)=sqrt3 lie (a) ...

    Text Solution

    |

  18. The number of real roots of the equation cos e ctheta+sectheta-sqrt(15...

    Text Solution

    |

  19. If =lt=xlt=2pi, then the number of solutions of 3(sinx+cosx)-(sin^3x+c...

    Text Solution

    |

  20. If 2sin^2((pi/2)cos^2x)=1-cos(pis in2x),x!=(2n+1)pi/2,n in I , then c...

    Text Solution

    |