Question

verify: sin(x+y)-sin(x-y)=2cosxsiny

Answer 1

cos(x+y)=cosxacosy-sinxsiny
cos(x-y)=cosxcosy+sinxsiny
addition produces 2cosxcosy

Answer 2

take the left hand side...do you know the formula for sin(x+y) and sin(x-y)?

Answer 3

Its an identity.

Answer 4

i think so but i'm not sure

Answer 5

sin(x+y) = sinxcosy + sinycosx

sin(x-y) = sinxcosy - sinycosx

can you do it from here?

Answer 6

it looks familiar but i can't figure it out. is it one of the cosine identities?

Answer 7

no...you substitute those into your problem

sin(x+y) - sin (x-y) = sinxcosy + cosxsiny - (sinxcosy - cosxsiny)

Answer 8

i'm still confused

Answer 9

with what?

Answer 10

how to do all of this in general

Answer 11

basically you memorize the identities...

Answer 12

i did not do anything fancy...all i did was substitute identities

Answer 13

oh ok

Answer 14

so regarding this problem...you're good?

Answer 15

not really...

Answer 16

sinxcosy + cosxsiny - (sinxcosy - cosxsiny)

sinxcosy = cosxsiny - sinxcosy + cosxsiny

Answer 17

that's a + not an =

Answer 18

i don't understand what you did

Answer 19

i distributed the minus sign

Answer 20

oh ok i see

Answer 21

so you're good now?

Answer 22

yes thanks ^^