求值(1+tan1°)(1+tan2°)·······﹙1+tan44°﹚

2025-02-25 12:54:05
推荐回答(1个)
回答1:

1=tan45°=tan(1°+44°)=(tan1°+tan44°)/(1-tan1°tan44°)
=>tan1°+tan44°=1-tan1°tan44°
=>tan1°+tan44°+tan1°tan44°+1=1+1
=>(1+tan1°)(1+tan44°)=2
同理
(1+tana)[1+tan(45°-a)]=2
(1+tan1°)(1+tan2°)·······﹙1+tan44°﹚
=(1+tan1°)(1+tan44°)(1+tan2°)(1+tan43°)...(1+tan22°)(1+tan23°)
=2^22