Question

∫f(x)sinxdx =∫f(x)cosxdx = 0，积分限0-π，则f（x）在0→π有两个零

∫f(x)sinxdx =∫f(x)cosxdx = 0，积分限0-π，则f（x）在0→π有两个零点

Answer 1

f(x)sinxdx =0,∫f(x)cosxdx =0 (0,π)
let
y = π-x
dy = -dx
∫f(x)cosxdx =0 (0,π)
∫f(π-y)cosy(-dy) =0 (π,0)
∫f(π-x)cosxdx =0 (0,π)
=> ∫ (f(π-x) - f(x) ) cosx =0 (0,π)
similarly
∫ (f(π-x) - f(x) ) sinx =0 (0,π)
（0，派）内f(x)至少有两个零点.

追问

请解释similarly下面的意思