if sin x = 1/3 and sec y = 5/4 , where x and y lie between 0 and π/2, evaluate sin(x + y).

If the sec y = 5/4, than the cosy  = 4/5

And   cosx =   sqrt(3^2  - 1^2) / 3 =   sqrt(8)/3

And siny  = 3/5

And

So....

sin(x + y)  =

sinxcosy  + sinycosx =

(1/3)(4/5) +  (3/5)(sqrt(8)/3  =

[4 + 3sqrt(8)] / 15