You got wrong answers because you thought

cos(a+B) = cos(a) +cosB, and sin(a-B) = sin(a) -sinB.

No.

The correct expansions are:

cos(a+B) = cos(a)*cosB -sin(a)*sinB.

And, sin(a-B) = sin(a)*cosB -cos(a)*sinB

So, get all the sines and cosines of angles "a" and B, then solve your questions again. You will get them this time.