If sin(x) = 4/5 and cos(y) = 5/13 with both x and y terminating in quadrant 1 find the exact value of cos(x-y)

Question

I know that the denominator will be 65

Answer 1

Use Pythagoras for each to find

i
sinx = 4/5, then cosx = 3/5
if cosy = 5/13, then siny = 12/13

cos(x-y) = cosxcosy + sinxsiny
= (3/5)(5/13) + (4/5)(12/13)
= (15+48)/65 = 63/65