求(1/1-tan22.5°)-(1/1+tan22.5°)的值

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求(1/1-tan22.5°)-(1/1+tan22.5°)的值

求(1/1-tan22.5°)-(1/1+tan22.5°)的值
求(1/1-tan22.5°)-(1/1+tan22.5°)的值

求(1/1-tan22.5°)-(1/1+tan22.5°)的值
解:
1/(1-tan22.5º)-1/(1+tan22.5º)
=(1+tan22.5º-1+tan22.5º)/(1+tan22.5º)(1-tan22.5º)
=2tan22.5°/(1-tan²22.5°)
=tan(2x22.5º)
=tan45º
=1

答:1/(1-tan22.5°)-1/(1+tan22.5°)
=(1+tan22.5°)/[(1-tan22.5°)(1+tan22.5°)-(1-tan22.5°)/[(1+tan22.5°)(1-tan22.5°)]
=(1+tan22.5°-1+tan22.5°)/(1-tan²22.5°)
=2tan22.5°/(1-tan²22.5°)
=tan45°
=1