If `p in (0, pi)`, then the complete set of values of `p` for which `sin p cos^3 p > sin^3 p cosp` always hold good, is

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If p in (0, pi) then the set of values of p for which sin p* cos^(3) p gt sin^(3) p*cos p holds, is ________.

Number of values of p for which equation sin^(3)x+1+p^(3)-3p sin x=0(p>) has a root is

Number of values of p for which equation sin^3x+1+p^3-3 p sinx=0 (p >0) has a root is ________

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Find the smallest positive number p for which the equation cos (p sin x) = sin (p cos x) has a solution x in [0,2pi] .