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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 belongs to [0,2 π ]
pie/4
cos(psinx)=sin(pcosx)sin(π/2 – psinx)=sin(pcosx)π/2 – psinx = pcosxp(sinx + cosx)= π/2p(root2)(sin(x+π/4))=π/2(sin(x+π/4))=π/2p(root2) since sine lies b/w -1 and 1therefore, -1π/2(3/2)pthe positive value of p is to be takenso, 1(3/2)p/πhence the minimum value of p is (π/2(3/2)) approve if useful by the way @akshat the spelling of π is pi and not pie ;) ; )
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