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 values of p for which the equation 1+p sin x=p^(2)-sin^(2)x has a solution

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

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

Smallest positive x satisfying the equation sin3x+3cos x=2sin2x(sin x+cos x), is-

The value of p for which the equation 3 " sin"^(2)x + 12 "cos" x - 3 =p has at least one solution are

The number of solutions that the equation sin (cos (sin x))= cos (sin (cos x)) has in [0, (pi)/(2)], is "_____"

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

Prove that sin1>cos(sin1). Also,show that the equation sin(cos(sin x))=cos(sin(cos x)) has only one solution in [0,(pi)/(2)]

Find the number of solution of the equation sqrt(cos 2x+2)=(sin x + cos x) in [0, pi] .