∵AD平分∠BAC∴∠BAD=∠CAD=1/2∠BAC=1/2(180°-∠B-∠C)=90°-1/2∠B-1/2∠C∵AE⊥BC∴∠BAE=90°-∠B∴∠DAE=∠BAD-∠BAE =90°-1/2∠B-1/2∠C-90°+∠B =1/2(∠B-∠C)
∠DAE = 1/2∠BAC - ∠BAE=1/2(180-∠B-∠C) - (180-90-∠B)=90-1/2∠B-1/2∠C-90+∠B=1/2(∠B-∠C)