If sinx 13 and secy 53 where x and y lie between 0 and 2 e

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

sinx = 1/3 ; secy = 5/3 x and y lie between 0 and pi/2

sin(x +y) = sinx *cosy +siny*cosx

sinx = 1/3 ; cosx = 2sqrt(2)/3

cosy = 3/5 ; siny = 4/5

So, sin(x +y) = sinx *cosy +siny*cosx

= (1/3)(3/5) +(4/5)(2sqrt(2)/3)

= (3 + 8sqrt(2) )/15

= [ 3 +8sqrt2]/15