Question

已知tan（

π

4

+α）=2，求

1

2sinαcosα+cos2α

的值．

Answer 1

由tan(

π

4

+α)=

1+tanα

1-tanα

=2，得tanα=

1

3

.
于是

1

2sinαcosα+cos2α

=

sin2α+cos2α

2sinαcosα+cos2α

=

tan2α+1

2tanα+1

=

( 1 3 )2+1

2× 1 3 +1

=

2

3

.