Question

已知a属于(0,π),sina+cosa=1/5.求①sina*cosa②sina-cosa③tan（a-π/2）

Answer 1

(sina+cosa)^2=1/25

2sinacosa=1/25-sin^2+cos^2=-24/25

sinacosa=-12/25

(sina-cosa)^2=sin^2+cos^2-2sinacosa

=49/25

因为a∈（0,π）所以sina

sina-cosa=-7/5

tan（a-π/2）=tana

sina+cosa=1/5

sina-cosa=-7/5

合并sina=-3/5,cosa=4/5

tana=sina/cosa=-3/4