If `x in [0,2pi]`, then `y=sinx/|sin x|, y=|cos x|/cos x` are identical functions for `x in`

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)

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)

int_(0)^(pi//2) (sinx )/(sin x + cos x ) dx=

If x in [0. (pi)/(2)], y in [0, (pi)/(2)] and sin x + cos y =2, then the value of x+y is equal to

If cos x + cos y =2 , then the value of sinx + sin y is

If x in[0,pi//2] y in [0,pi//2] and sin x + cos y = 2, then the value of x + y is equal to

If sinx + sin y=(1)/(2) and cos x+cos y=1 , then tan (x+y)=

Consider a function f (x) in [0,2pi] defined as : f(x)=[{:([sinx]+ [cos x],,, 0 le x le pi),( [sin x] -[cos x],,, pi lt x le 2pi):} where {.} denotes greatest integer function then. Number of points where f (x) is non-derivable :

The number of distinct real roots of the equation, |(cos x, sin x , sin x ),(sin x , cos x , sin x),(sinx , sin x , cos x )|=0 in the interval [-pi/4,pi/4] is :

If x sin y+y cos x=pi , then the value of y''(0) is -