`f(x)=(s i x)/(sqrt(1+tan^2x))+(cos x)/(sqrt(1+cot^2x))` is constant in which of following interval a.`\ (0,\ pi/2)` b. `(pi/2,\ pi)` c. `(pi,\ ((3pi)/2)` d. `((3pi)/2,2pi)`

If x in [0,2pi]" then "y_(1)=(sin x)/(|sin x|), y_(2)=(|cos x|)/(cos x) are identical functions for x in : I. (0,pi/2)" "II. (pi/2, pi)," "III. (pi,(3pi)/(2))," "IV. ((3pi)/(2),2pi)

f (x) = cos ((pi) / (sqrt (3)) sin x + sqrt ((2) / (3)) pi cos x)

The smallest positive root of the equation tan x-x=0 lies in (0,(pi)/(2)) (b) ((pi)/(2),pi)(pi,(3 pi)/(2)) (d) ((3 pi)/(2),2 pi)

f(x) = cos x is strictly increasing in the interval : (a) ((pi)/(2),pi) (b) (pi,(3 pi)/(2)) (c) (0,(pi)/(2))

One of the root equation cos x-x+(1)/(2)=0 lies in the interval (0,(pi)/(2))(b)(-(pi)/(2,0))(c)((pi)/(2),pi)(d)(pi,(3 pi)/(2))

The value of sectheta/sqrt(1-cos^2x)+cosx/(sqrt(1+cot^2theta))" for "theta in (pi,(3pi)/2) is

If y=tan^(-1)x+tan^(-1)(1/x)+sec^(-1)x , then y lies in the interval (a) [pi/2,pi)uu[pi,(3pi)/2) (b) [pi/2,(3pi)/2] (c)(0,pi) (d) [0,pi/2)uu[pi/2,pi)

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))

If f(x)=A sin((pi x)/(2))+b,f'((1)/(2))=sqrt(2) and int_(0)^(1)f(x)dx=(2A)/(pi), then constants A and B are (pi)/(2)and(pi)/(2) (b) (2)/(pi) and (3)/(pi)0 and -(4)/(pi) (d) (4)/(pi) and 0

which of the following statement is // are true ? (i) f(x) =sin x is increasing in interval [(-pi)/(2),(pi)/(2)] (ii) f(x) = sin x is increasing at all point of the interval [(-pi)/(2),(pi)/(2)] (3) f(x) = sin x is increasing in interval ((-pi)/(2),(pi)/(2)) UU ((3pi)/(2),(5pi)/(2)) (4) f(x)=sin x is increasing at all point of the interval ((-pi)/(2),(pi)/(2)) UU ((3pi)/(2),(5pi)/(2)) (5) f(x) = sin x is increasing in intervals [(-pi)/(2),(pi)/(2)]& [(3pi)/(2),(5pi)/(2)]