f(sina+cosa)=sinacosa f(cos30度)=
问题描述：
f(sina+cosa)=sinacosa f(cos30度)=
答
f(sina+cosa)=sinacosa
=sin^2a/2+cos^2a/2+sinacosa^2-1/2
=(sina+cosa)^2/2-1/2
=[(sina+cosa)^2-1]/2
f(x)=(x^2-1)/2
f(cos30度)
=[(cos30度)^2-1]/2
=[3/4-1]/2
=(-1/4)/2
=-1/8
答
f(sina+cosa)=sinacosa
令sina+cosa=t
1+2sinacosa=t²
sinacosa=(t²-1)/2
所以
f(t)=(t²-1)/2
f(cos30度)=f(√3/2)=-1/8