How can I show f(x)=x(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}-cosx=0 has exactly 2 solutions? I can show it has at least two by using the fact that f is even and continuous and f(0)<0 and f(1)>0 so there's at least one solution in 0<x<1 and thus one solution in -1<x<0. I'm trying to derive a contradiction by assuming there's a third solution but I can't seem to find one.

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# How can I show f(x)=x2-cosx=0 has exactly 2 solutions?

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