Question

if secx - tanx = 2/3 ,then sex= ? and tanx = ?

Answer 1

we know,
sec²A - tan²A = 1
(secA - tanA)(secA + tanA) = 1

given,
(secx - tanx) = 2/3 ------(1)
so, sec²x - tan²x = 1
(secx + tanx)(secx - tanx ) = 1
(secx + tanx)(2/3) = 1
secx + tanx = 3/2 -------(2)

solve equations (1) and (2)
2secx = 2/3 + 3/2 = (4 + 9)/6 = 13/6
secx = 13/12

put it in equation (1)
tanx = 5/13

hence, tanx = 5/13 and secx = 13/12

Answer 2

Hope it will help you .