Question

已知tan（π/4+a）=2,求1/[2sinacosa+(cosa)^2]的值

Answer 1

tan(π/4+a)

=(tanπ/4+tana)/(1-tanπ/4tana)

=(1+tana)/(1-tana)

=2

1+tana=2-2tana

3tana=1

tana=1/3

1/(2sinacosa+cos²a)

=(sin²a+cos²a)/(2sinacosa+cos²a)

分子分母同时除以cos²a

=(tan²a+1)/(2tana+1)

=(1/9+1)/(2/3+1)

=2/3