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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 ]

Find the smallest positive number p for which the equation cos(p sin x)= sin( p cos x) has a solution x belongs to [0,2π]

Grade:Select Grade

2 Answers

grenade
2061 Points
8 years ago
pie/4
AUREA
61 Points
8 years ago
cos(psinx)=sin(pcosx)
sin(π/2 – psinx)=sin(pcosx)
π/2 – psinx = pcosx
p(sinx + cosx)= π/2
p(root2)(sin(x+π/4))=π/2
(sin(x+π/4))=π/2p(root2)
 
since sine lies b/w -1 and 1
therefore, -1π/2(3/2)p
the positive value of p is to be taken
so, 1(3/2)p/π
hence 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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