设t=x-π/2
左边=∫(-π/2,π/2)f(丨cos(t+π/2)丨)dt
=∫(-π/2,π/2)f(丨sint丨)dt
因为f(丨sint丨)是偶函数
所以=2∫(0,π/2)f(丨sint丨)dt
又因为0<=t<=π/2时,sint>=0
所以=2∫(0,π/2)f(sinx)dx=右边