`Iff(x)={s i^(-1)(sinx),x >0pi/2,x=0,t h e ncos^(-1)(cosx),x<0` `x=0` is a point of maxima `x=0` is a point of minima `x=0` is a point of intersection `non eoft h e s e`

If f(x)={sin^(-1)(sinx),xgt0 (pi)/(2),x=0,then cos^(-1)(cosx),xlt0

If x in (0,pi/2), then show that cos^(-1)(7/2(1+cos2x)+sqrt((sin^2x-48cos^2x))sinx)=x-cos^(-1)(7cosx)

If |cos^(-1)((1-x^2)/(1+x^2))|

Find the point of discontinuity of the function f(x)={:{(sinx,x lt 0),(1-cosx,0 le xle pi),(cosx, x gtpi):}

If f(x)=cosx-int_0^x(x-t)f(t)dt ,t h e nf^(primeprime)(x)+f(x) is equal to (a) -cosx (b) -sinx (c) int_0^x(x-t)f(t)dt (d) 0

Let f(x) = |(2cos^2x, sin2x, -sinx), (sin2x, 2 sin^2x, cosx), (sinx, -cosx,0)| , then the value of int_0^(pi//2){f(x) + f'(x)} dx is

if f(x)= sinx + cosx for 0 < x < pi/2

Which of the following is/are true? (dy)/(dx)fory=sin^(-1)(cosx),w h e r ex in (0,pi),i s-1 (dy)/(dx)fory=sin^(-1)(cosx),w h e r ex in (0,2pi),i s1 (dy)/(dx)fory=cos^(-1)(sinx),w h e r ex in (-pi/2,pi/2),i s-1 (dy)/(dx)fory=cos^(-1)(sinx),w h e r ex in (pi/2,(3pi)/2),i s-1

If f(x)=sqrt(1-sin2x) , then f^(prime)(x) is equal to (a) -(cosx+sinx),forx in (pi/4,pi/2) (b) cosx+sinx ,forx in (0,pi/4) (c) -(cosx+sinx),forx in (0,pi/4) (d) cosx-sinx ,forx in (pi/4,pi/2)

int _0^(pi/2) (sin^2x)/(sinx+cosx)dx