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Work Step by Step
Assume that $ f(x)= x-\cos x $, then we show that $ f(x)$ has a zero $[0,1]$. Indeed, since the function $ f(x)=x-\cos x $ is continuous on $[0,1]$ and $ f(0)=-1 <0$ and $ f(1)=1 -\cos 1 > 0$ then by the bisection method $ f(x)$ has a zero in the interval $(0,1)$. Hence $ x=\cos x $ has a solution in $[0,1]$.