We know that
sin (x + y) = sin x cos y + cos x sin y ... (1)
Now cos2x = 1 – sin2x = 1 – 9/25 = 16/25
Therefore cos x = ± 4/5.
Since x lies in second quadrant, cos x is negative.
Hence cos x = −4/5
Now sin2y = 1 – cos2y = 1 – 144/169 = 25/169
i.e. sin y = ± 5/13.
Since y lies in second quadrant, hence sin y is positive.
Therefore, sin y =5/13.
Substituting the values of sin x, sin y, cos x and cos y in (1), we get
sin(x + y) 3/5 × (-12/13) + (−4/5) × 5/13 = (-36/65) –(20/65) = -56/65
Therefore, sin(x+y) = -56/65