Question

Trig/ Pre Cal/ identities Am I on the right path? Please do not give answer but guide me. Thank you.

cos(x - y) - cos(x+y) = 2sin x siny

Is cos(x-y) like
cos(a-B) = cos a cos B + sin a sin B

Answer 1

yes

Answer 2

cos(x-y) like
cos(a-B) = cos a cos B + sin a sin B

Answer 3

just plug x and y into a and b

Answer 4

Ok, this does not seem to work.

cos x *cos y + sin y *sin y - cos x * cos y - sin x * sin y = 2sin x 2 sin y

Should be 2sin x sin y.

Am I skipping something?

Answer 5

cos(x+y) is not like cos(x-y)

Answer 6

cos(x+y) = cos x cos y - sin x sin y

Answer 7

yah your angle sum and different expansions look correct nixy :)
do you see the next step after that?

Answer 8

oh oh oh, i think you simply forgot to distribute the negative.

Answer 9

\[\Large\rm \cos(x-y)\color{red}{-}\cos(x+y)\]\[\Large\rm =\cos x \cos y+ \sin x \sin y \color{red}{-}(\cos x \cos y -\sin x \sin y)\]

Answer 10

Ah ok I see. man it was right in front of me. The way you put it made it clearer lol

Answer 11

Thanks @zepdrix and @Thesn1

Answer 12

np