Question

(1+tan21°)(1+tan22°)(1+tan23°)(1+tan24°)=_________________.

Answer 1

解析:(1+tan21°)(1+tan24°)

=1+tan21°+tan24°+tan21°·tan24°

=1+tan(21°+24°)(1-tan21°tan24°)+tan21°·tan24°=2.

同理,(1+tan22°)(1+tan23°)=2.

∴原式=4.

答案:4