Home
Class 12
MATHS
The function f(x)""=""t a n^(-1)(sinx""+...

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)`

A

`(pi/4, pi/2)`

B

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

C

`(0, pi/2)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MONOTONOCITY

    MOTION|Exercise Exercise - 2 (Level-I) ( Objective Problems ) ( FINDING VALUE OF VARIABLE GIVEN MONOTONIC BEHAVIOUR)|3 Videos
  • MONOTONOCITY

    MOTION|Exercise Exercise - 2 (Level-I) ( Objective Problems ) ( CHECKING MONOTONOCITY AT POINT OR IN AN INTERVAL )|2 Videos
  • MONOTONOCITY

    MOTION|Exercise Exercise - 1 ( Objective Problems ) ( SECTION-H & I : CURVE SKETCHING, QUESTION ON FINDING NUMBER OF SOLUTION )|4 Videos
  • METHOD OF DIFFERENTIATION

    MOTION|Exercise EXERCISE - 4 LEVEL -II|5 Videos
  • PARABOLA

    MOTION|Exercise EXERCISE - IV|33 Videos

Similar Questions

Explore conceptually related problems

The function f(x)=tan^(-1)(sin x+cos x) is an increasing function in (1)((pi)/(4),(pi)/(2))(2)(-(pi)/(2),(pi)/(4))(3)(0,(pi)/(2))(4)(-(pi)/(2),(pi)/(2))^(((pi)/(4)),(pi)/(2))^(((pi)/(4)))(2)

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

Prove the following f(x)=tan^(-1)(sinx+cosx) is strictly decreasing function on ((pi)/(4),(pi)/(2)) .

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

Show that f(x)=cos(2x+pi/4) is an increasing function on (3 pi/8,7 pi/8)

Show that f(x)=cos(2x+(pi)/(4)) is an increasing function on (3 pi/8,7 pi/8)

The largest interval lying in (-pi/2,pi/2) for which the function [f(x)=4^-x^2+cos^(-1)(x/2-1)+log(cosx)] is defined, is (1) [0,pi] (2) (-pi/2,pi/2) (3) [-pi/4,pi/2) (4) [0,pi/2)

If cos(sinx)=0, then x lies in (a) (pi/4,pi/2)uu(pi/2,\ pi) (b) (-pi/4,\ 0) (c) (pi,(3pi)/2) (d) null set

The range of function f(x)=cot^(-1)x+sec^(-1)x+ cosec^(-1)x is (A) [(pi)/(2), pi)uu(pi, (3 pi)/(2)] (B) ((pi)/(2), (3 pi)/(4)] uu [(5 pi)/(4), (3 pi)/(2)) (C) ((pi)/(2), pi)uu(pi ,(3 pi)/(2)) (D) ((pi)/(2), (3 pi)/(2))

f:R rarr R , f(x)=tan^(-1)(2^x) + k is an odd function, then k= (A) -pi/4 (B) (pi)/(4) (C) -(pi)/(2) (D) (pi)/(2)