若α,β为锐角,且α+β=45° 求证(1+tanα)(1+tanβ)=2
问题描述:
若α,β为锐角,且α+β=45° 求证(1+tanα)(1+tanβ)=2
(2)求log2(1+tan1°)+log2(1+tan2°)+···log2(1+45°)=?
答
tan(a+b)=1tana+tanb=1-tana*tanb tana+tanb+tana*tanb=1(1+tanα)(1+tanβ)=1+tana+tanb+tana*tanb=2--------------------------------------------由 1=tan45°=(tan1°+tan44°)/(1-tan1°tan44°),得 tan1°+tan...