Find the values of p for which the equation `1+p sinx=p^2-sin^2x` has a solution

The smallest positive real value of p for which the equation cos (p sin x) = sin (p cos x) has a solution where x in [0, 2pi] is

The range of the values of p for which the equation sin cos^(-1)(cos(tan^(-1)x))=p has a solution is

The range of value of p for which the equation sincos^(-1)(cos(tan^(-1)x))=p has a solution is

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

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] .

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

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] .

Find all the values of p for which the equation x^(4)-4x^(3)-8x^(2)+p=0 has all real solutions

Find all the values of p for which the equation x^(4)-4x^(3)-8x^(2)+p=0 has two real solutions

Find all the values of p for which the equation x^(4)-4x^(3)-8x^(2)+p=0 has no real solution