cos(A-B)=cosA cosB + sinA sinB
if A=x and B=2x, that works

Here's something to calm you down.
I had my last exam on Friday. One week before the exam, the prof told us that "the questions would be mostly objective type with one case study question to solve."

2 hours before the exam, she finally gave the entire modalities of the exam and that's when we found out that she had completely changed the pattern and it was 100% subjective.

when k=1, the (stuff) under the ∑ evaluates to 20.
when k=2, the (stuff) under the ∑ evaluates to 20.
...
when k=80, the (stuff) under the ∑ evaluates to 20.
and so you add up all the results

∑(20- (1/4)k)
= ∑(20) - ∑(k/4)
= ∑(20) - (1/4)∑k
= 20·80 - (1/4)(80·81)/2
= 1600 - 810
= 790

(6/n)sum((i/n+1)
(6/n)[sum(i/n)+sum(1)]
(6/n)[(1/n)sumi+n] <---- sum(1)=n
(6/n)[(1/n)*n(n+1)/2)+n]
(6/n)[((n+1)/2)+n)]
(6/n)[3n+1/2]
(18n+6)/2n
(9n+3)/n
9+3/n