Answer:
Part 1) 
Part 2) 
Part 3) 
Part 4) 
Part 5) 
Part 6) 
Step-by-step explanation:
<u><em>the complete answer in the attached document</em></u>
Part 1) we have


Determine cos (A+B)
we know that

step 1
Find the value of cos(A)
Remember that

substitute the given value





The angle A belong to the I quadrant, the cosine is positive

step 2
Find the value of sin(B)
Remember that

substitute the given value





The angle B belong to the I quadrant, the sine is positive

step 3
Find cos(A+B)
substitute in the formula



Part 2) we have


Determine cos (A-B)
we know that

step 1
Find the value of cos(A)
Remember that

substitute the given value





The angle A belong to the I quadrant, the cosine is positive

step 2
Find the value of sin(B)
Remember that

substitute the given value





The angle B belong to the I quadrant, the sine is positive

step 3
Find cos(A-B)
substitute in the formula



Part 3) we have


Determine cos (A-B)
we know that

step 1
Find the value of cos(A)
Remember that

substitute the given value





The angle A belong to the I quadrant, the cosine is positive

step 2
Find the value of sin(B)
Remember that

substitute the given value





The angle B belong to the I quadrant, the sine is positive

step 3
Find cos(A-B)
substitute in the formula



Part 4) we have

Determine cos (A+B)
we know that

step 1
Find the value of cos(A)
Remember that

substitute the given value




The angle A belong to the I quadrant, the cosine is positive

step 2
Find the value of sin(B)
Remember that

substitute the given value





The angle B belong to the I quadrant, the sine is positive

step 3
Find cos(A+B)
substitute in the formula


