c3 question on trig proof

Also, there was this question I was confused about :

Use the identities for cos (A + B) and cos (A − B) to prove that
2cos A cos B ≡ cos (A + B) + cos (A − B).

Would i be OK by doing this:

cos (A + B) + cos (A-B)= cos A cos B - sinA sin B +cos A cos B + sinA sinB

you end up with 2cosA cos B because those sin thingies will cancel out . Would this way of proof be OK since the mark scheme is saying something a bit diff? This is the mark scheme answer:

cos (A + B) ≡ cos A cos B − sin A sin B
cos (A − B) ≡ cos A cos B + sin A sin B
adding, 2 cos A cos B ≡ cos (A + B) + cos (A − B

Also, there was this question I was confused about :

Use the identities for cos (A + B) and cos (A − B) to prove that
2cos A cos B ≡ cos (A + B) + cos (A − B).

Would i be OK by doing this:

cos (A + B) + cos (A-B)= cos A cos B - sinA sin B +cos A cos B + sinA sinB

you end up with 2cosA cos B because those sin thingies will cancel out . Would this way of proof be OK since the mark scheme is saying something a bit diff? This is the mark scheme answer:

cos (A + B) ≡ cos A cos B − sin A sin B
cos (A − B) ≡ cos A cos B + sin A sin B
adding, 2 cos A cos B ≡ cos (A + B) + cos (A − B

What you're saying and what the mark scheme is saying is essentially the same