Question

(1+tan21°)(1+tan20°)(1+tan25°)(1+tan24°)的值是(    )

A．2         B．4          C．8            D．16

Answer 1

B

解析：∵1=tan45°=tan (21°+24°)

=

∴1-tan21°tan24°=tan21°+tan24°,

即tan21°+tan24°+tan21°tan24°=1,

∴(1+tan21°)(1+tan24°)= tan21°+tan24°+tan21°tan24°+1=2,

同理(1+tan20°)(1+tan25°)=2,

∴(1+tan21°)(1+tan20°)(1+tan25°)(1+tan24°)=2×2=4.