How do I do this by sketching a triangle.
sin( arcsin(1/2) + arccos(1/2) )
let's start with arcsin(1/2)
draw a right angled triangle where theta and alpha are the two angles other than the 90º angle.
suppose you make the opposite side 1, and the hypotenuse 2.
Now look at the other angle alpha. Wouldn't the cosine of that angle also be 1/2??
(if you know your 30º, 60º, 90º triangle ratios, you will realize that the two angles are 30 and 60)
but since theta + alpha must total 90º, you are really just being asked for sin 90º, which is 1
so the answer is 1