If `log_(cosx) sinx>=2` and `x in [0,3pi]` then `sinx` lies in the interval

If log_(cosx)sin x ge 2 and 0le xle 3pi , then the value of sinx lies in the interval (0, (sqrta-b)/(2)] then value of a-b is

The number of distinct real roots of the equation |{:(cosx, sinx, sinx), (sinx, cosx, sinx), (sinx, sinx, cosx):}|=0 in the interval [-\ pi/4,pi/4] is- a. 3 b. \ 4 c. \ 2 d. 1

If log_(cosx)sinx+log_(sinx)cosx=2 , then x =

Statement-1: f(x ) = log_( cosx)sinx is well defined in (0,pi/2) . and Statement:2 sinx and cosx are positive in (0,pi/2)

Statement-1: f(x ) = log_( cosx)sinx is well defined in (0,pi/2) . and Statement:2 sinx and cosx are positive in (0,pi/2)

The number of distinct real roots of |(sinx, cosx, cosx),(cosx, sinx, cosx),(cosx, cosx, sinx)|=0 in the interval -(pi)/4le x le (pi)/4 is

The number of distinct roots of abs((sinx, cosx, cosx),(cosx, sinx, cosx),(cosx, cosx, sinx))=0 in the interval -pi/4 le x le pi/4 is

If, x,y inR , then the determinant: Delta=|(cosx,-sinx,1),(sinx,cosx,1),(cos(x+y),-sin(x+y),0)| lies in the interval .