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

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)]

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 eqution sin x+x cos=0 has at least one root in (A)(-(pi)/(2),0)(B)(0,pi)(C)(pi,(3 pi)/(2)) (D) (0,(pi)/(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 that function given by f(x)=sin x is (i) Strictly increasing in (-(pi)/(2),(pi)/(2)) (ii) Strictly decreasing in ((pi)/(2),(3pi)/(2))

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)

If |veca+vecb|lt|vecavecb| then the angle between veca and vecb lies in the interval (A) (-pi/2, pi/2) (B) (0,pi0) (C) (pi/2,(3pi)/2) (D) (0,2pi)

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))

Prove that the function f(x)=cos x is strictly increasing in (pi,2 pi)

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