If A = arc sin -3/5 and B = arccos 7/25 what is sin(A+B) & cos(A-B)

We'll apply the
formula:

sin(A+B) = sin A*cos B + sinB*cos
A

sin A = sin[arcsin (-3)/5] =
-3/5

cos B = cos [arccos 7/25] =
7/25

sin B = sqrt(1 - 49/625) = sqrt(576/625) =
24/25

cos A = sqrt(1 - 9/25) = sqrt(16/25) =
4/5

sin(A+B) = (-3/5)*(7/25) + (24/25)*(4/5) = (96-21)/125
= 75/125 = 3/5

We'll apply the formula for the cosine of
difference of 2 angles:

cos(A-B) = cos A*cos B + sin A*sin
B

We'll just substitute the values found out
earlier:

cos(A-B) = 4*7/5*25 +
(-3*24)/5*25

cos(A-B) = (28 - 72)/5*25 =
-44/125

The values for sin(A+B) and cos(A-B)
are: sin(A+B) = = 3/5 , cos(A-B) = -44/125.