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

来源：学生作业学帮网编辑：学帮网时间：2024/05/14 12:27:05

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.