If α, β are acute angles such that Sin = 1/12 and Cos β = 4/5

Calculate the six trigonometric functions for the sum and differences of the two angles….

Did you mean ? There's no angle in the first one, and I'm going to assume you meant .

Do you have trig identities for the sum and difference of angles? e.g. and such?

I suggest that you think of the givens in terms of right triangles, and use SOHCAHTOA and the pythagorean theorem to find and .

Then use the identities to compute the sine and cosine of the summed and differenced angles, and from there try to get all six trigonometric functions.