sin(x) = 1/2 in the first quadrant => x = 30°
cos(y) = (√2) / 2 in the first quadrant => y = 45°
=> x + y = 75°
=> tan (x + y) = tan (75°) = 3.73
Also you can use:
tan (x +y) = sin(x + y) / cos(x + y)
sin (x + y) = sin(x)cos(y) + cos(x)sin(y)
sin(x) = 1/2 in the first quadrant => cos(x) = (√3) / 2
cos(y) = √2 / 2 in the first quadrant => sin(xy = √2 / 2
=> sin(x+y) = (1/2)(√2/2) + (√3)/2 (√2)/2 = √2 / 4 + √6 / 4
cos(x + y) = cos(x) cos(y) - sin(x)(sin(y) = (√3)/2 (√2)/2 - (1/2)(√2)/ 2 = √6 /4 - √2 / 4
=> tan(x +y) = [√2 / 4 + √6 /4] / [√6 / 4 - √2 / 4] = [√2 + √6] / [√6 - √2] = 3.73