解tan675°+1/tan765°-sin(-5π/2)+1/cos(-23π/6)
=tan(720°-45°)+1/tan(720°+45°)+sin(5π/2)+1/cos(23π/6)
=tan(-45°)+1/tan(45°)+sin(2π+π/2)+1/cos(4π-π/6)
=-tan(45°)+1/1+sin(π/2)+1/cos(-π/6)
=-1+1+1+1/(cos(π/6))
=1+1/(√3/2)
=1+2√3/3
tan675°+1/tan765°-sin(-5π/2)+1/cos(-23π/6)
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