Home
Class 12
MATHS
Show that f(x) =tan^(-1)(sinx+cosx) is a...

Show that f(x) `=tan^(-1)(sinx+cosx)` is an increasing function in `(0,pi/4)`.

A

`(-(pi)/(2),(pi)/(4))`

B

`(-(pi)/(4),(pi)/(4))`

C

`((5pi)/(4),(3pi)/(2))`

D

`(-2pi,-(7pi)/(4))`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|8 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS ENGLISH|Exercise Exercise (Passage Based Questions)|33 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Option Correct Type Questions)|27 Videos

  • MATRICES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|49 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

Similar Questions

Explore conceptually related problems

The function f(x)=tan^(-1)(sinx+cosx) is an increasing function in

Show that f(x)=tan^(-1)(sinx+cosx) is an increasing function on the interval (0,\ pi//4) .

The function f(x)=tan^(-1)(sinx+cosx) is an increasing function in (-pi/2,pi/4) (b) (0,pi/2) (-pi/2,pi/2) (d) (pi/4,pi/2)

Show that f(x)=tan^(-1)(sinx+cosx) is decreasing function on the interval (pi/4,pi/2)dot

Show that f(x)=tan^(-1)(sinx+cosx) is a decreasing function on the interval on (pi//4,\ pi//2) .

The function f(x)""=""t a n^(-1)(sinx""+""cosx) is an increasing function in (1) (pi/4,pi/2) (2) (-pi/2,pi/4) (3) (0,pi/2) (4) (-pi/2,pi/2)

Show that f(x)=sinx-cosx is an increasing function on (-pi//4,\ pi//4) .

Show that f(x)=sinx is an increasing function on (-pi//2,\ pi//2) .

Show that f(x)=tanx is an increasing function on (-pi//2,\ pi//2) .

Show that the function f(x)=cot^(-1)(sinx+cosx) is decreasing on (0,\ pi//4) and increasing on (pi//4,\ pi//2) .

ARIHANT MATHS ENGLISH-MONOTONICITY MAXIMA AND MINIMA-Exercise (More Than One Correct Option Type Questions)
  1. Which of the following is/are true? (you may use f(x)=ln((lnx))/(lnx...

    Text Solution

    |

  2. If underset(xrarra)(lim)f(x)=underset(xrarra)(lim)[f(x)] ([.] denotes ...

    Text Solution

    |

  3. Let S be the set of real values of parameter lamda for which the equat...

    Text Solution

    |

  4. h(x)=3f((x^2)/3)+f(3-x^2)AAx in (-3, 4) where f''(x)> 0 AA x in (-3,4)...

    Text Solution

    |

  5. Let f(x)=log(2x-x^2)+sin(pix)/2dot Then which of the following is/are ...

    Text Solution

    |

  6. Show that f(x) =tan^(-1)(sinx+cosx) is an increasing function in (0,pi...

    Text Solution

    |

  7. If the maximum and minimum values of the determinant |(1 + sin^(2)x...

    Text Solution

    |

  8. Let f(x)={:{(x^(2)+4x",",-3lexle0),(-sinx",",0ltxle(pi)/(2)),(-cosx-1"...

    Text Solution

    |

  9. Let f(x)=ab sin x+bsqrt(1-a^(2))cosx+c, where |a|lt1,bgt0 then

    Text Solution

    |

  10. If f(x)=int(x^(m))^(x^(n))(dt)/(lnt),xgt0andngtm, then

    Text Solution

    |

  11. f(x)=sqrt(x-1)+sqrt(2-x) and g(x)=x^(2)+bx+c are two given functions s...

    Text Solution

    |

  12. Find the intervals in which f(x)=6x^2-24x+1 increases and decreases

    Text Solution

    |

  13. A function f is defined by f(x)=int(0)^(pi)cos t cos (x-t)dt, 0 lexle2...

    Text Solution

    |

  14. Let f(x) be a differentiable function on the interval (-oo,0) such tha...

    Text Solution

    |

  15. If f: R rarr R , f ( x) is differentiable bijective function then whic...

    Text Solution

    |

  16. Let f:(0,oo)rarr(0,oo) be a derivable function and F(x) is the primiti...

    Text Solution

    |