Question

I really need help with this Trig identity please!(Grade 12!)

How do I prove that sinx-siny = 2cos([x+y]/2)sin([x+y]/2)

Answer 1

I've been at it for so long! I cant get it :(

Answer 2

I can help.

Answer 3

Thank you so much

Answer 4

We have only learnt compound angles, by the way

Answer 5

So there is an identity that's called co function identies, do you know them?

Answer 6

I think so

Answer 7

Or sum to product identities. Do any of these sound familiar.

Answer 8

Is it the cos(90-x) kind of thing?

Answer 9

um, not really. Here, let me post a link.

Answer 10

http://www.sosmath.com/trig/Trig5/trig5/trig5.html

Answer 11

Thanks Ill read it!

Answer 12

nope....never learnt those :s

Answer 13

Okay.

Answer 14

Give me like 5-10 minutes. This one is a little tricky. I'll try to keep you updated with the steps.

Answer 15

Alright I really appreciate it

Answer 16

I found a note that our teacher wrote on the board! I dont get it though...

he wrote

Answer 17

sinx + siny = sin(a+b) = sinacosB + cosAsinB
sin(a-b) = sinAcosB - cosAsinB

sin(a+B) + sin (a - b) = 2sinAcosB

Answer 18

ignore the caps they are the same letter

Answer 19

Then he wrote : let : a+b = x
a - b = y


2a = x+y
x = (x+y)/2

Answer 20

still working....

Answer 21

Okay, Do you know the double angle formula?

Answer 22

yep!

Answer 23

good.

Answer 24

okay, so cos([x+y]/2)sin([x+y]/2).

This equal sin(x+y)

Answer 25

Are you following what i mean here?

Answer 26

hmm

Answer 27

how about this.
2cosAsinA=sin2a. A=(x+y)/2

Answer 28

alright

Answer 29

cosine of x is sine of (90-x) right?

Answer 30

yep

Answer 31

okay. so
=sin(x+y)
=sinxcosy+sinycosx
=sinx sin(90-y)+siny sin(90-x)

Answer 32

yep

Answer 33

I have a quick question, is it sin(x+y)/2 or sin(x-y)/2?

Answer 34

one sec for the original question?

Answer 35

yes.

Answer 36

oh no! you are right it sin(x-y)!!!!!!!

Answer 37

sorry ><

Answer 38

Ok, that makes more sense now.

Answer 39

Give me another minute to type this up.

Answer 40

Of course

Answer 41

ok, i've got it.

Answer 42

:D

Answer 43

ok let me know if you can see it.

Answer 44

I can see it! Im following through fine so far. Thank you so much

Answer 45

Yep.