Question

高一数学 有关函数

1.若(1+tanx)/(1-tanx)=2008,则1/cos2x+tan2x等于______
2.（1+tan17°)(1+tan28°)=_______

Answer 1

1.1/cos2x+tan2x=(1+sin2x)/cos2x
=(sinx+cosx)^2/(cos^2x-sin^2x)
=(sinx+cosx)/(cosx-sinx)
=(1+tanx)/(1-tanx)
=2008
2.（1+tan17°)(1+tan28°)=1＋tan17°+tan28°＋tan17°tan28°
tan45°=tan(17°+28°)
=(tan17°+tan28°)/(1-tan17°tan28°)=1
tan17°+tan28°=1-tan17°tan28
tan17°+tan28°＋tan17°tan28°=1
(1+tan17°)(1+tan28°)=2