secx+tgx=22/7cscx+ctgx=m/n,其中m/n是既约分数,则m+n=?

Question

secx+tgx=22/7 cscx+ctgx=m/n,其中m/n是既约分数,则m+n=?

Answer 1

(1+sin(x))/cos(x) = 22/7
(1+cos(x))/sin(x) = m/n = ctg(x/2)
22/7 = ctg(pi/4 - x/2)
令u = pi/4 - x/2
22/7 = ctg(u)
m/n = ctg(pi/4 -u) = 1/tg(pi/4-u) = (ctg(u)+1)/(ctg(u)-1) =
= 29/15
m+n=44