if sin(x) = 1/3 and sec(y) = 25/24
, where x and y lie between 0 and π/2, evaluate the expression using trigonometric identities. (enter an exact answer.)

what i know:
cos (y) = 25/24
sin (x + y) = (sinx)(cosy) + (cosx)(siny)

sin (x + y) = (1/3)(24/25) + (cosx)(siny)

how do you get cosx and siny?

.

We can approach this in another way.
We know that sin(∅) = height / hypotenuse.

Thus, for x, height is 1 and hypotenuse is 3. Using Pythagoras theorem,
3² = 1² + b²
b = √8
cos(x) = b/hypotenuse
cos(x) = √8 / 3

Now, lets consider y:
sec(y) = 1 / cos(y) = 1 / base / hypotenuse = hypotenuse / base
The hypotenuse is 25 and the base is 24. We again apply Pythagoras theorem to find the third side, which works out to be:
height = 7
sin(y) = height / hypotenuse
sin(y) = 7/25

Now, sin(x + y) =
sin(x)cos(y) + sin(y)cos(x)
= (1/3)(24/25) + (√8 / 3)(7/25)
= 8/25 + 7√8/75
= (24 + 14√2) / 75

Cis the