show that there is a number x between 0 and pi/2 such that cosx=x.

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show that there is a number x between 0 and pi/2 such that
cosx=x

Aarushi Mishra · Accepted Answer

Dear studentLet fx=cos x-xf0=cos 0-0=1>0fπ2=cos π2-π2=-π2<0Since fx is continuous in 0,π2, therefore, there must exist some value of x between 0 and π2 such that fx=0