sin(30°+α)×tan(135°+α)×tan(135°-α)×1/cos(60°-α)
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sin(30°+α)×tan(135°+α)×tan(135°-α)×1/cos(60°-α)

= (sin 30°cos α +cos 30°sin α) ×{(tan135° +tanα) /(1-tan135°tanα)}×{(tan135° -tanα) /(1+tan135°tanα)}×1/(cos60°cos α+sin60°sinα)

= {1/2cos α+(根号3)/2sinα}×{(-1+tanα)/(1+tanα)}×{ (-1-tanα)/ (1-tanα) }× 1/{ (1/2cos α+(根号3)/2sinα

= {(-1+tanα)/(1+tanα)}×{ (-1-tanα)/ (1-tanα) }

=1

tan135°=tan(180°-45°)= -tan45°=-1