exsin‌x‌=1 f(x)‌=sin‌x−e−x Let it has 2 real roots α,β f′(x)=cos‌x+e−x=0 Using Rolle's theorem There will be at least one real root of its derivative between α and β At least one c∈(α,β) f′(c)‌=0 e−c+cos‌c‌=0 1+ec‌cos‌c‌=0=g(c) g(x)‌=ex‌cos‌x+1 α‌<c<b At least one real root of g(x) between two real root of f(x).