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## Homework Statement

[itex]\sin (x) = \frac{2}{3}[/itex] and [itex]\sec (y) = \frac{5}{4}[/itex], where [itex]x[/itex] and [itex]y[/itex] lie between 0 and [itex]\frac{\pi}{2}[/itex] evaluate [itex]\sin (x + y)[/itex]

## Homework Equations

Looked over some trig laws, don't think I saw anything that's too relevant. There [itex]\sec (x) = \frac{1}{\sin (x)}[/itex]

## The Attempt at a Solution

I can't think of anything. Assuming I'm not an idiot, I can simply re-write the secant equation as another sine equation:

[tex]\sec (y) = \frac{5}{4} \longrightarrow \sin (y) = \frac{4}{5}[/tex]

So then we know [itex]\sin (x) = \frac{2}{3}[/itex] and [itex]\sin (y) = \frac{4}{5}[/itex]. From here we can do some inverse sines and substitute in [itex]x[/itex] and [itex]y[/itex] in [itex] \sin (x+y)[/itex], but that looks awful and worse to solve ([itex]\sin (\sin ^{-1} (\frac{2}{3}) + \sin ^{-1} (\frac{4}{5})[/itex]).

Can anyone give me a hint as to the proper next step I should take to evaluate this equation?

Thanks for any help!