Number of the solutions of `sin x=[1+sinx]+[1-cosx]`

If [.] represents greatest integer function then find the number of solution in the equation sinx=[1+sinx]+[1-cosx] in [0,2pi]

Number of solutions of |x-1|=cosx is

The number of solutions of sin x+cos.x=sin^(-1)x+cos ec^(-1)x is

Total number of solutions of sin^(4)x+cos^(4)x=sinx*cosx in [0,2pi] is equal to

In the interval [-pi/4,pi/4] the number of real solutions of the equations |[sinx , cosx ,cosx],[cosx, sinx, cosx],[cosx , cosx , sinx]| =0

Number of solutions of the equation log_("sinx + cosx") sqrt2 - (-1 + 2sin2x) = 0 where x in [0, 2pi] , is _______

General solution of cosx-sinx=1 is

Number of solution of equation y=1/3[sinx+[sinx+[sinx]]] and [y+[y]]=2cosx is/are