已知sin(3π+θ)=lg1/(10开3次方) 求{cos(π+θ)/cosθ[cos(π-θ)-1]}+{ cos(θ-2π)/sin(θ-3π/2)cos(θ-π)-sin(3π/2+θ)}的值

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已知sin(3π+θ)=lg1/(10开3次方) 求{cos(π+θ)/cosθ[cos(π-θ)-1]}+{ cos(θ-2π)/sin(θ-3π/2)cos(θ-π)-sin(3π/2+θ)}的值

sin(3π+θ)=lg1/10^(1/3)=lg10^(-1/3)=-1/3
sin(3π+θ)=sin(π+θ)=-sinθ
所以sinθ=1/3
原式=[-cosθ/[cosθ(-cosθ-1)]+[cosθ/cosθ(-cosθ)+cosθ]
=1/(1+cosθ)+1/(1-cosθ)
=(1-cosθ+1+cosθ)/sin²θ
=2/(1/3)²
=18