Question

化簡(jiǎn)

(sinx+cosx-1)(sinx-cosx+1)

sin2x

．

Answer 1

分析：先根據(jù)三角函數(shù)的二倍角公式，再分子分母同時(shí)除以2sin

x

2

，可得答案．

解答：解：原式=

(sinx+1-2sin2 x 2 -1)(sinx-1+2sin2 x 2 +1)

sin2x

=

(2sin x 2 cos x 2 -2sin2 x 2 )(2sin x 2 cos x 2 +2sin2 x 2 )

4sin x 2 cos x 2 cosx

=

(cos x 2 -sin x 2 )(cos x 2 +sin x 2 )•sin x 2

cos x 2 cosx

=

(cos2 x 2 -sin2 x 2 )sin x 2

cos x 2 •cosx

=

cosx•sin x 2

cos x 2 •cosx

=tan

x

2

．

點(diǎn)評(píng)：本題主要考查三角函數(shù)的二倍角公式的應(yīng)用．二倍角公式在考查三角函數(shù)時(shí)時(shí)重點(diǎn)考查對(duì)象要給予重視．