Question

高一三角化简

Answer 1

(1+tan(a/2))/(1-tan(a/2))

=cos(a/2)*(1+tan(a/2))/[cos(a/2)*(1-tan(a/2))]

=(cos(a/2)+sin(a/2))/(cos(a/2)-sin(a/2)) ①

=(cos(a/2)+sin(a/2))²/[(cos(a/2)-sin(a/2))*(cos(a/2)+sin(a/2))]

=(cos(a/2)+sin(a/2))²/[(cos(a/2)-sin(a/2))*(cos(a/2)+sin(a/2))] ②

=(1+2sin(a/2)cos(a/2))/(cos²(a/2)-sin²(a/2))

=(1+sina)/cosa