Question

已知tan(派/4+α）=2,求1/（2sinαcosα+cos平方α）的值.

Answer 1

tan(α+π/4)=(tanα+tanπ/4)/(1-tanαtanπ/4).

=(tanα+1)/(1-tanα)=2.

tanα+1=2-2tanα.

3tanα=1

tanα=1/3.

1/(2sinαcosα+cos^2α)=(1/cos^2α)/(2tanα+1).

=sec^2α/(2tanα+1).

=(1+tan^2α)/(2tanα+1)

=[1+(1/3)^2]/[2*(1/3)+1].

=(10/9)/(5/3)

=2/3.----即为所求.