If `log_(0.5) sin x=1-log_(0.5) cos x,` then the number of solutions of `x in[-2pi,2pi]` is

log_(sqrt(3))(sin x+2sqrt(2)cos x)>=2,-2 pi<=x<=2 pi then the number of value of x, is

The total number of solutions of log_e |sin x| = -x^2 +2x in [0,pi] is equal to

The total number of solutions of log_e |sin x| = -x^2 +2x in [0,pi] is equal to

The total number of solutions of log_e |sin x| = -x^2 +2x in [0,pi] is equal to

The total number of solutions of log_e |sin x| = -x^2 +2x in [0,pi] is equal to

If log_(0.5)log_(5)(x^(2)-4)>log_(0.5)1, then' x' lies in the interval

Suppose that x is a real number with log_(5)(sin x)+log_(5)(cos x)=-1. The value of |sin^(2)x cos x+cos^(2)x sin x| is equal to

The number of distinct solutions of the equation [log_((1)/(2))|sin x|=2-log_((1)/(2))|cos x| in the interval "[0,2 pi]" is

If log_((1)/(sqrt(2)))sin x>0,x in[0,4 pi], then the number values of x which are integral multiples of (pi)/(4), is