Question

已知函数f（x）=cos²[（π/4）+ x] - cos²[（π/4）- x]。则f（π/12）等于（ ）

Answer 1

f(x)=cos²(π/4+x)—cos²(π/4—x)
=cos²(π/4+x)—sin²(π/4+x)
=cos2(π/4+x)=cos(π/2+2x)
= -sin2x
f(π/12)= -sinπ/6= -1/2

Answer 2

解：
易知，cos²(π/4-x)=-cos²(x-π/4+2π)=-cos²(x+π/4+π/2)=sin²(x+π/4)
∴f(x)=cos²(π/4+x)-sin²(π/4+x)
=cos2(π/4+x)=cos(π/2+2x)
= -sin2x
∴f(π/12)= -sinπ/6= -1/2