`cosx-sinx=sqrt2 cos(x+pi/4)`

The number of integers in the range of the function f(x)=|4((sqrt(cosx)-sqrt(sinx))(sqrt(cosx)+sqrt(sinx)))/((cosx+sinx))| is ________.

The number of integers in the range of the function f(x)=|4((sqrt(cosx)-sqrt(sinx))(sqrt(cosx)+sqrt(sinx)))/((cosx+sinx))| is ________.

I : int_(0)^(pi//2)(sqrtcotx)/(sqrt(tanx)+sqrt(cotx))dx=(pi)/(4) II : int_(0)^(pi//2)(2sinx+3cosx)/(sinx+cosx)dx=(pi)/(4)

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

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

Differentiate cos^(-1){(cosx+sinx)/(sqrt(2))},\ -pi/4

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)

Differentiate the functions with respect to x : cos^(-1){(cosx+sinx)/(sqrt(2))},-pi/4ltxltpi/ 4

int_0^(pi/4) (cos x- sin x) dx + int_(pi/4)^((5pi)/4) (sinx-cosx) dx + int_(2pi)^(pi/4) (cosx- sinx) dx =

int_(0)^(pi//2)(sqrt(sinx))/((sqrt(sinx)+sqrt(cosx)))dx=(pi)/(4)