trigonometry

I believe that the answer is 1.05.

To expand upon Guest's answer:

sec(x) + tan(x)  =  5/2     --->     1 / cos(x)  +  sin(x) / cos(x)  =  5/2

Multiplying each side by  2·cos(x)   --->         2( 1 + sin(x) )  =  5( cos(x) )

Squaring both sides:                      4( 1 + 2sin(x) + sin²(x) )  =  25cos²(x)

Since  cos²(x) = 1 - sin²(x):                4 + 8sin(x) + 4sin²(x)  =  25 - 25sin²(x)

Rewriting:                                        29sin²(x) + 8sin(x) - 21  =  0

Quadratic formula:                                                      sin(x)  =  [ -8 +/- sqrt(2500) ] / 58

Choosing the positive answer:                                    sin(x)  =  42/58

Taking the opposite side as 42 and the hypotenuse as 58, 

by the Pythagorean formula, the adjacent side will be 40,

which means that the value of tangent is 42 / 40  =  1.05.