Trigonometry help

If
sin(x) = 1/3 and sec(y) = 13/12
, where x and y lie between 0 and π/2, evaluate the expression using trigonometric identities. (Enter an exact answer.)
sin(x + y)

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  1. since both x and y are in quadrant I, everything will stay positive
    make sketches of right-angled triangles for each case

    from sinx = 1/3, cosx = √8/3

    from secy = 13/12 ---> cosy = 12/13
    then siny = 5/13

    sin(x+y) = sinxcosy + cosxsiny
    = (1/3)(12/13) + (√8/3)(5/13)
    = (12+5√8)/39 or
    = (12 + 10√2)/39

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  2. please correct cosx = - square 8/3

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