Question

化简f(x)=(√(sin(x/2))^4+4(cos(x/2))^2))-(√(cos(x/2))^4+4(sin(x

Answer 1

sin(x/2)^4=(1-cos(x/2)^2)^2

所以sin(x/2)^4+4(cos(x/2))^2=(1+cos(x/2)^2)^2

同理cos(x/2)^4+4(sin(x/2))^2=(1+sin(x/2)^2)^2

所以f(x)=(1+cos(x/2)^2)-(1+sin(x/2)^2)=cos(x/2)^2-sin(x/2)^2=cos(x)

f(a)+f(a/2)=0

也就是cos(a)=-cos(a/2)=cos(π-a/2)

考虑到0