Question

已知tan

α

2

=3，求cos(

π

2

+α)=______．

Answer 1

∵cos(

π

2

+α)=sinα=2sin

α

2

cos

α

2

=

2sin α 2 •cos  α 2

sin2 α 2 +cos2 α 2

=

2tan α 2

1+tan2 α 2

，把tan

α

2

=3 代入可得
cos(

π

2

+α)=

6

1+9

=

3

5

．
故答案为：

3

5

．