Home
Class 12
MATHS
The function f(x)=tan^(-1)(sinx+cosx) is...

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)`

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos
  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

The function f(x)=tan^(-1) (sin x+ cos x) is an increasing function in (-pi/2, pi/k) , then find k.

Range of tan^(-1)((2x)/(1+x^2)) is (a) [-pi/4,pi/4] (b) (-pi/2,pi/2) (c) (-pi/2,pi/4) (d) [pi/4,pi/2]

Let f:(-1,1)rarrB be a function defined by f(x)=tan^(-1)[(2x)/(1-x^2)] . Then f is both one-one and onto when B is the interval. (a) [0,pi/2) (b) (0,pi/2) (c) (-pi/2,pi/2) (d) [-pi/2,pi/2]

tan^(-1)[(cosx)/(1+sinx)] is equal to pi/4-x/2,when (a) x in (-pi/2,(3pi)/2) (b) x in (-pi/2,pi/2) (c) x in (-pi/2,pi) (d) x in (-(3pi)/2,pi/2)

If roots of the equation 2x^2-4x+2sintheta-1=0 are of opposite sign, then theta belongs to (pi/6,(5pi)/6) (b) (0,pi/6)uu((5pi)/6,pi) ((13pi)/6,(17pi)/6) (d) (0,pi)

Prove that the function f given by f(x) = log sin x is increasing on (0,(pi)/(2)) and decreasing on ((pi)/(2),pi) .

Range of the function f(x)=sqrt(cos^(- 1)(sqrt(log_4x))-pi/2)+sin^(- 1)((1+x^2)/(4x)) is equal to (A) (0,pi/2+sqrt(pi/2)] (B) [pi/2,pi/2+sqrt(pi/2)] (C) [pi/6,pi/4) (D) {pi/6}

Show that the function given by f (x) = sin x is (a) increasing in (0,(pi)/(2)) (b) decreasing in ((pi)/(2) ,pi) (c) neither increasing nor decreasing in (0, pi )

The maximum value of the function f(x)=sin(x+pi/6)+cos(x+pi/6) in the interval (0,pi/2) occurs at (a) pi/(12) (b) pi/6 (c) pi/4 (d) pi/3

If 0lexle2pi , the function f(x) = sinx is minimum at -

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Let f be a continuous, differentiable, and bijective function. If the ...

    Text Solution

    |

  2. Let f(x)=xsqrt(4a x-x^2),(a >0)dot Then f(x) is (a). increasing in (0,...

    Text Solution

    |

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

    Text Solution

    |

  4. A function is matched below against an interval where it is supposed t...

    Text Solution

    |

  5. On which of the following intervals is the function f given by f(x) = ...

    Text Solution

    |

  6. Let g(x)=2f(x/2)+f(2-x)a n df^('')(x)<0AAx in (0,2)dot Then g(x) ...

    Text Solution

    |

  7. Let f: R->R be a differentiable function for all values of x and has...

    Text Solution

    |

  8. Which of the following statement is always true? (a)If f(x) is incre...

    Text Solution

    |

  9. The function f(x)=sum(k=1)^5 (x-K)^2 assumes then minimum value of x g...

    Text Solution

    |

  10. The function x^x decreases in the interval (a) (0,e) (b) (0,1) (c) (...

    Text Solution

    |

  11. Let f(x)=|x^2-3x-4|,-1lt=xlt=4 Then a) f(x) is monotonically increasin...

    Text Solution

    |

  12. If f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x) then f(x) (a)increase in (...

    Text Solution

    |

  13. Let x and y be two real variable such that x >0 and x y=1 . Find the m...

    Text Solution

    |

  14. A box, constructed from a rectangular metal sheet, is 21 cm by 16cm by...

    Text Solution

    |

  15. A wire of length a is cut into two parts which are bent, respectively,...

    Text Solution

    |

  16. The maximum area of the rectangle whose sides pass through the vertice...

    Text Solution

    |

  17. The vertices of a triangle are (0,0), (x ,cosx), and (sin^3x ,0),w h ...

    Text Solution

    |

  18. Assertion Let f:R→R,f(x)=x^3+x^2+3x+sinx f(x) is one-one. Reason f(x) ...

    Text Solution

    |

  19. The base of prism is equilateral triangle. The distance from the centr...

    Text Solution

    |

  20. Let f(x)=2x-sinx and g(x)=3sqrtx . Then

    Text Solution

    |