已知函数f(x)=4COS^4x-2COS2x-1/SIN(TT/4+x)SIN(TT/4-x)求f(-11TT/12)
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已知函数f(x)=4COS^4x-2COS2x-1/SIN(TT/4+x)SIN(TT/4-x)求f(-11TT/12)的值
![已知函数f(x)=4COS^4x-2COS2x-1/SIN(TT/4+x)SIN(TT/4-x)求f(-11TT/12)](/uploads/image/z/4255336-64-6.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%EF%BC%9D4COS%5E4x-2COS2x-1%2FSIN%28TT%2F4%2Bx%29SIN%28TT%2F4-x%29%E6%B1%82f%28-11TT%2F12%29)
f(-11π/12)=4cos^4(11π/12)-2cos(11π/6)+1/sin(7π/6)sin(2π/3)
sin2π/3sin(7π/6)=-sinπ/6sinπ/3=-√3/4
2cos11π/6=2cos(2π-π/6)=2cosπ/6=√3
4cos^4x=(2cos^2x)^2=(1+cos2x)^2
cos2x=cos22π/12=√3/2
(1+√3/2)^2=(1/4)(4+2√3)=1+√3/2
f(-11π/12)=1+√3/2-√3-4/√3
=1-11√3/6
sin2π/3sin(7π/6)=-sinπ/6sinπ/3=-√3/4
2cos11π/6=2cos(2π-π/6)=2cosπ/6=√3
4cos^4x=(2cos^2x)^2=(1+cos2x)^2
cos2x=cos22π/12=√3/2
(1+√3/2)^2=(1/4)(4+2√3)=1+√3/2
f(-11π/12)=1+√3/2-√3-4/√3
=1-11√3/6
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