" If "10g_(0.5)sin x=1-log_(0.5)cos x" then number of values of "x in[-2 pi,2 pi]" is "

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

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

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

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

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

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

If [sin x]+[(x)/(2 pi)]+[(2x)/(5 pi)]=(9x)/(10 pi), then number of values of x in (30,40) is

Number of values of x satisfying the equation log_(2)(sin x)+log_((1)/(2))(-cos x)=0 in the interval (-pi,pi), is equal to -

If for x in (0, (pi)/(2) ) , log _(10) sin x + log _(10) cos x =-1 and log _(10) (sin x + cos x) = (1)/(2) ( log _(10) n-1), n gt 0, then the value of n is equal to :

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