Geometry problem

I think it's 4/5

tan x + sec x =  2

sin x / cos x  + 1 /cosx  = 2

[ sinx + 1 ]  = 2 cosx             square both sides

sin^2 x  + 2sinx + 1 =  4cos^2x

sin^2x + 2sinx + 1  = 4 (1 - sin^2x)

5sin^2x + 2sinx - 3  =  0       factor as

(5sinx - 3) (sinx + 1) =  0 

5sinx - 3 = 0             sinx + 1 =  0

5sinx = 3                  sinx = -1   (reject as x = -pi/2)

sinx = 3/5

cos x  =  sqrt [ 5^2 - 3^2 ] /  5  =   sqrt [ 16 ] / 5  =   4 / 5