yww566353
幼苗
共回答了22个问题采纳率:90.9% 举报
(1)∵AD=AB
∴∠D=∠ABD
∴∠BAC=∠D+∠ABD=2∠D
∴∠D=∠BAC/2
∵AC=BC
∠C=90°
∴∠BAC=45°
∴∠D=45°/2=22.5°
(2)令AC=BC=1
∴AB=√2
∴CD=1+√2
∴tan∠D
=1/(1+√2)
=(√2-1)/[(√2+1)(√2-1)]
=√2-1
(3)∵∠D=22.5°
∠C=90°
∴∠CBD=67.5°
∴tan67.5°
=tan∠CBD
=CD/BC
=1+√2
∴tan67.5°×cos45°-sin45°
=(1+√2)×(√2/2)-√2/2
=√2/2+1-√2/2
=1
1年前
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