令t=x-π/2，则dx=dt左边=∫(-π/2,π/2) (t+π/2)f(cost)dt=∫(-π/2,π/2) t*f(cost)dt+∫(-π/2,π/2) (π/2)*f(cost)dt因为t*f(cost)是奇函数，(π/2)*f(cost)是偶函数所以左边=(π/2)*∫(-π/2,π/2) f(cost)dt将x=t+π/2代回左边=(π/2)*∫(0,π) f(sinx)dx=右边
