Home
Class 12
MATHS
The general solution of cos x cos 6x =-1...

The general solution of `cos x cos 6x =-1` is

A

`x=(2n+1) pi, n in Z`

B

`x=2n pi, n in Z`

C

`x= n pi, n in Z`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`cos x cos 6x=-1`
or `2 cos x cos 6x=-2`
or `cos 7x+ cos 5x=-2`
or `cos 7x =-1 and cos 5x=-1`
The value of x satisfying these two equations simultaneously and lying between 0 and `2pi` is `pi`.
Therefore, the general solution is `x=2npi+pi, n in Z`. Thus,
`x=(2n+1) pi, 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|34 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

Similar Questions

Explore conceptually related problems

The general solution of cos x cos6x=-1 is x=(2n+1)pi,n in Zx=2n pi,quad n in Zx=n pi,n in Z(d) none of these

General solution of cos2x=0 is

General solution of cos3x=cos2x is

The general solution of sin2x=4cos x is

Find the general solution of : cos x - sin x = 1 .

The general Solution of (sin x+cos x)>=1 is

General solution of 2cos2x=-1 is

Find the general solution of sin5x cos 3x = sin9x cos7x

Find the general solution of Sin x-Cos x = 1 .

General solution of cos7x=cosx-sin4x is

CENGAGE-TRIGONOMETRIC EQUATIONS-Exercise (Single)
  1. Let alphaa n dbeta be any two positive values of x for which 2cosx ,|c...

    Text Solution

    |

  2. The number of values of theta satisfying 4 cos theta+3 sin theta=5 as ...

    Text Solution

    |

  3. The general solution of cos x cos 6x =-1 is

    Text Solution

    |

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

    Text Solution

    |

  5. Let theta in [0,4pi] satisfy the equation (sintheta+2)(sintheta+3)(sin...

    Text Solution

    |

  6. The number of solutions of sum(r=1)^5cosrx=5 in the interval [0,2pi] i...

    Text Solution

    |

  7. If cos 3x+sin (2x-(7pi)/6)=-2, then x is equal to (k in Z)

    Text Solution

    |

  8. The general solution of the equation sin^100 x - cos^100 x =1 is (wher...

    Text Solution

    |

  9. The sum of all the solutions in [0, 4pi] of the equation tan x+ cot x+...

    Text Solution

    |

  10. The total number of solutions of loge |sin x| = -x^2 +2x in [0,pi] is...

    Text Solution

    |

  11. The total number of solution of sin{x}=cos{x} (where {} denotes the fr...

    Text Solution

    |

  12. The set of all xin((-pi)/2,pi/2) satisfying |4sinx-1|<sqrt(5) is given...

    Text Solution

    |

  13. If roots of the equation 2x^2-4x+2sintheta-1=0 are of opposite sign, t...

    Text Solution

    |

  14. If |2 sin theta-cosec theta| ge 1 and theta ne (n pi)/2, n in Z, then

    Text Solution

    |

  15. Which of the following is not the solution of the equation sin 5x=16 s...

    Text Solution

    |

  16. The number of solutions of the equation |2 sin x-sqrt(3)|^(2 cos^(2)...

    Text Solution

    |

  17. One root of the equation cos x-x+1/2=0 lies in the interval (A...

    Text Solution

    |

  18. The smallest positive x satisfying the equation (log)(cosx)sinx+(log)(...

    Text Solution

    |

  19. The number of ordered pairs which satisfy the equation x^2+2xsin(x y)+...

    Text Solution

    |

  20. Consider the system of linear equations in x, y, and z: (sin 3 theta...

    Text Solution

    |