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)`

A

`(0,pi//2)`

B

`(0,(pi)/(2))`

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
1
Here fX() =`tan^(-1) (sinx+cosx)`
`therefore f(X)=(1)/(1+(sinx+cosx)^(2)(cosx-sinx)`
`=(cosx-sinx)/(2+sin 2 x)`
`for -(pi)/(2)ltxlt(pi)/(4),cos x gtsinx`
Hence y = f(X) is increasing in `(-(pi)/(2),(pi)/(4))`
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|48 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Linked comprehension type|50 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercise 6.7|5 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|7 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Comprehension Type|6 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-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Exercise
  1. A function is matched below against an interval where it is supposed t...

    Text Solution

    |

  2. On which of the following intervals is the function x^(100)+sinx-1 dec...

    Text Solution

    |

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

    Text Solution

    |

  4. Assertion Consider the following statements in S and R S: Both sinx a...

    Text Solution

    |

  5. The length of the longest interval in which the function 3sinx-4sin^3x...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Function f(x)=|x|-|x-1| is monotonically increasing when (a) x<0 (b) ...

    Text Solution

    |

  9. If f^(prime)(x)=|x|-{x}, where {x} denotes the fractional part of x , ...

    Text Solution

    |

  10. The length of the largest continuous interval in which the function f(...

    Text Solution

    |

  11. f(x)=(x-2)|x-3| is monotonically increasing in (-oo,5/2)uu(3,oo) (b)...

    Text Solution

    |

  12. f(x)=(x-8)^4(x-9)^5,0lt=xlt=10 , monotonically decreases in (a) (76/9...

    Text Solution

    |

  13. For all x in (0,1) (a) e^x<1+x (b) (log)e (1+x) < x (c) sin x > x (d) ...

    Text Solution

    |

  14. If f(x)=x e^(x(x-1)) , then a) f(x) is increasing on [-1/2,1] b) decre...

    Text Solution

    |

  15. If f(x)=k x^3-9x^2+9x+3 monotonically increasing in R , then

    Text Solution

    |

  16. If the function f(x)=(Ksinx+2cosx)/(sinx+cosx) is strictly increasing ...

    Text Solution

    |

  17. Let f: RvecR be a function such that f(x)=a x+3sinx+4cosxdot Then f(x)...

    Text Solution

    |

  18. Which of the following statement is always true? If f(x) is increasing...

    Text Solution

    |

  19. Let f: RvecR be a differentiable function for all values of x and has ...

    Text Solution

    |

  20. Let f: Rvec be a differentiable function AAx in R . If the tangent dr...

    Text Solution

    |