Home
Class 12
MATHS
Solve |sinx +cos x |=|sinx|+|cosx|, x in...

Solve `|sinx +cos x |=|sinx|+|cosx|, x in [0,2pi]`.

Text Solution

Verified by Experts

The given relation holds only when sin x and cos x have the same sign or at least one of them is zero.
Hence, `x in [ 0, pi//2] cup [pi,3pi//2] cup {2pi}.`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.1|15 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.2|5 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise JEE Previous Year|12 Videos

  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|28 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Solve |sinx+cosx|=|sinx|+|cosx|,x in [0,2pi]dot

Solve sinx +cosx =1

Solve sinx-cosx +sqrt2=0 .

The number of solution of 2cosx=|sinx| where x in [0.4pi] is/are

Separate the intervals of monotonocity for the function f(x)=sinx+cosx ,x in (0,2pi)

Solve: |-2x^2+1+e^x+sinx|=|2x^2-1|+e^x+|sinx|,x in [0,2pi]dot

prove that [2(sin^3 x - cos^3 x )/(sinx -cosx)]-sin2x=2

CENGAGE-RELATIONS AND FUNCTIONS-Examples
  1. Solve: (-1)/(|x|-2) ge 1.

    Text Solution

    |

  2. Solve |x-1|+|x-2| ge 4

    Text Solution

    |

  3. Solve |sinx +cos x |=|sinx|+|cosx|, x in [0,2pi].

    Text Solution

    |

  4. Solve: |-2x^2+1+e^x+sinx|=2x^2-1|+e^x+|sinx|,x in [0,2pi]dot

    Text Solution

    |

  5. Let A= (1, 2, 3, 4, 6). Let R be the relation on A defined by {(a,b) a...

    Text Solution

    |

  6. If R={(x,y): x,y in W, x ^(2)+y^(2)=25}, then find the domain and rang...

    Text Solution

    |

  7. If R(1)={(x,y)|y=2x+7, where x in R and -5 le x le 5} is a relation. T...

    Text Solution

    |

  8. Show that the relation R in the set R of real numbers, defined as R={...

    Text Solution

    |

  9. Show that the relation R in the set Z of intergers given by R ={(a,...

    Text Solution

    |

  10. Show that the relation R in the set A of points in a plane given by R...

    Text Solution

    |

  11. Show that the relation R defined in the set A of all triangles as R={(...

    Text Solution

    |

  12. Given a non-empty set X, consider P(X) which is the set of all subs...

    Text Solution

    |

  13. Examine each of the following relations given below and state in each...

    Text Solution

    |

  14. If A is set of different triangles in the plane and B is set of all po...

    Text Solution

    |

  15. A relation R is defined from N to N as R={(ab,a+b): a,b in N}. Is R ...

    Text Solution

    |

  16. Set A has m distinct elements and set B has n distinct elements. The...

    Text Solution

    |

  17. Write explicit functions of y defined by the following equations and a...

    Text Solution

    |

  18. Find the domain and range of the following functions. (i) f(x)=sqrt...

    Text Solution

    |

  19. Find the domain and range function f(x) =(x^(2)-3x+2)/(x^(2)-4x+3).

    Text Solution

    |

  20. Find the values of x for which the following functions are identical....

    Text Solution

    |