Question

函数解法已知f(1-cosx)=sinx的平方求f(x)

Answer 1

由cosx=1-2(sinx)^2得

1-cosx=2(sinx)^2

(sinx)^2=4(sinx/2)^2(cosx/2)^2,于是

f(1-cosx)=(sinx)^2可以写为

f(2(sinx)^2)=4(sinx/2)^2(cosx/2)^2=4(sinx/2)^2(1-(sinx/2)^2)

令2(sinx)^2＝t,(sinx)^2=t/2

f(t)=2t(1-t/2)

f(x)=2x(1-x/2)