设f(x)满足f(-sinx)+3f(sinx)=4sinx*cosx(x的绝对值小于等于π/2)

设x=sinx
f（-x）+3f（x）=4*x*√(1-x^2) .①
设x--sinx
f（x）+3f（-x）=4*（-x）*√(1-x^2).②
①②分别相加相减得到③④
4f（x）+4f（-x）=0.③
2f（x）-2f（-x）=8*x*√(1-x^2).④
③+④*2得
8f（x）=16*x*√(1-x^2)
f（x）=2*x*√(1-x^2)