Find the exact value of the expression sin arcsin 513 minus

Find the exact value of the expression: sin [arcsin 5/13 - (minus) arcos (-3/5)]

sin [arcsin 5/13 - (minus) arcos (-3/5)]

Let x= arcsin5/13 ;

sinx = 5/13 ---> cosx = 12/13---> x = arccos(12/13)

y = sqrccos(-3/5)

cosy = -3/5 ;

siny = 4/5 ---> y = arcsin4/5

sin(x-y) = sinxcosy - sinycosx

So, sin [arcsin 5/13 - (minus) arcos (-3/5)]

sinarcsin5/13 = 5/13 ; cosarccos(-3/5) = -3/5

sin [arcsin 5/13 - (minus) arcos (-3/5)] = sinxcosy +sinycosx

=(5/13)*(-3/5) - (4/5)(12/13)

= (-15 -48)/65

= -63/65

= 33/65