Home
Class 12
MATHS
The total number of solution of sin{x}=c...

The total number of solution of `sin{x}=cos{x}` (where `{}` denotes the fractional part) in `[0,2pi]` is equal to 5 (b) 6 (c) 8 (d) none of these

A

5

B

6

C

8

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`sin {x}=cos {x}`
`tan {x}=1`
`tan (pi//4)=1 lt tan 1`
Graphs of `y=tan {x}` and `y=1` meet exactly six times in `[0, 2pi]`.
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 period of function 2^({x})+sinpix+3^({x/2})+cos2pix (where {x} denotes the fractional part of (x) is 2 (b) 1 (c) 3 (d) none of these

The total number of solution of cosx=sqrt(1-sin2x) in [0,2pi] is equal to 2 (b) 3 (c) 5 (d) none of these

lim_(x to 0) {(1+x)^((2)/(x))} (where {.} denotes the fractional part of x) is equal to

lim_(x->oo ){(e^x+pi^x)^(1/x)}= where {.} denotes the fractional part of x is equal to

The domain of the function f(x)=1/(sqrt({sinx}+{sin(pi+x)})) where {dot} denotes the fractional part, is (a) [0,pi] (b) (2n+1)pi/2, n in Z (c) (0,pi) (d) none of these

The total number of solutions of [x]^2=x+2{x}, where [.] and {.} denote the greatest integer and the fractional part functions, respectively, is equal to: 2 (b) 4 (c) 6 (d) none of these

The total number of solutions of log_e |sin x| = -x^2 +2x in [0,pi] is equal to

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

The period of the function f(x)=(6x+7)+cospix-6x , where [dot] denotes the greatest integer function is: 3 (b) 2 pi (c) 2 (d) none of these

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

CENGAGE-TRIGONOMETRIC EQUATIONS-Exercise (Single)
  1. The sum of all the solution in [0,4pi] of the equation tanx+cotx+1=cos...

    Text Solution

    |

  2. The total number of solutions of (log)e|sinx|=-x^2+2x in [0,pi] is equ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. One of the root equation cosx-x+1/2=0 lies in the interval (a)(0,pi/2)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. Consider the system of linear equations in x , ya n dz : ""(sin3theta...

    Text Solution

    |

  13. The equation sin^4x-2cos^2x+a^2=0 can be solved if (a)-sqrt(3)lt=alt=s...

    Text Solution

    |

  14. If the inequality sin^2x+acosx+a^2>1+cosx holds for any x in R , then...

    Text Solution

    |

  15. sinx+cosx=y^2-y+a has no value of x for any value of y if a belongs to...

    Text Solution

    |

  16. The number of solutions of [sin x+ cos x]=3+ [- sin x]+[-cos x] (where...

    Text Solution

    |

  17. The equation cos^8x+bcos^4x+1=0 will have a solution if b belongs to (...

    Text Solution

    |

  18. The number of values of yin[-2pi,2pi] satisfying the equation |sin2x|+...

    Text Solution

    |

  19. If both the distinct roots of the equation |sinx|^2+|sinx|+b=0in[0,pi]...

    Text Solution

    |

  20. e^(|sinx|)+e^(-|sinx|)+4a=0 will have exactly four different solutions...

    Text Solution

    |