Find the exact value of the trig function below.

cos (x+y) if sinx =, cosx =, siny =, and cosy =

cos (x+y) = cos x. cos y - sin x. sin y

dа ta:

sin x=12/13

cos x=5/13

sin y=8/17

cos y=15/17

therefore:

cos (x+y) = cos x. cos y - sin x. sin y

cos (x+y) = (5/13) (15/17) - (12/13) (8/17)

cos (x+y) = 75/221-96/221

cos (x+y) = - 21/221

Answer: cos (x+y) = - 21/221

We can check it out our answer:

sin x=12/13

x=sin⁻¹ (12/13) ≈67.38

y=sin (8/17) ≈28.07

(x+y) = 67.38 + 28.07=95.45

(x+y) = cos⁻¹ (-21/221) = 95.45