+129771 sec x + tan x = 4/3
[ Note that tan^2 x + 1 = sec^2x → tan^2 x = sec ^2 x - 1 → tan x = sqrt ( sec^2 x - 1) ]
So
sec x + sqrt [sec^2 x - 1 ] = 4/3
sqrt [ sec^2 x - 1 ]= 4/3 - secx square both sides
sec^2 x - 1 = 16/9 - (8/3)sec x + sec^2 x simplify
-1 = 16/9 - (8/3)sec x rearrange as
(8/3)sec x = 16/9 + 1
(8/3)sec x = 25 / 9
sec x = (25/9)(3/8) = 75/72 = 25/24
cos x= 24/25
sin x = sqrt [ 25^2 - 24^2 ] / 25 = sqrt [ 49] / 25 = 7 / 25
