Question

sin(a+b)sin(a-b)=sin^2a-sin^2b

Answer 1

Open sin(a+b) and sin(a-b)

Answer 2

and end up with
sin^2Acos^2B-cos^2Asin^2b?

Answer 3

yes

Answer 4

then whats next

Answer 5

Notice that our final answer should contain only sin terms and not cosines

Answer 6

So change all cos x terms in terms of sin x

Answer 7

you could use the identity \[\sin^2 x+\cos^2 =1\]

Answer 8

there is no addition though when i expand???

Answer 9

Wait a sec ..pls I think there is a simpler way out

Answer 10

Gimme a minute

Answer 11

k

Answer 12

What is the problem in using \(cos^2(x) = 1- sin^2(x)\) there?? @AravindG

Answer 13

It seems the power becomes 4 when we use that here

Answer 14

yeah thats what i though

Answer 15

Oh yeah..

Answer 16

working on it ...

Answer 17

lo0l waterineyes your method actually worked

Answer 18

thanks man. If you expand it with your identities it works :)

Answer 19

How ?

Answer 20

They will cancel out I think.. ??

Answer 21

sin^2a - sin^2a sin^2b-sin^2b+sin^2a sin^2B
and they cancel out

Answer 22

\[\sin^2(A)- \sin^2(A)\sin^2(B) - \sin^2(B) + \sin^2(A)\sin^2(B)\]

Answer 23

yes

Answer 24

I was just doing calculations in mind, so that is why did not pick it up..:)

Answer 25

thanks man

Answer 26

Ya same here ...I mixed up the A and B ..Sorry

Answer 27

You are most welcome.. :)

Keep it up..

Answer 28

Yeah I too forgot when you say it will become 4, I did not check when you said. Earlier I had that we could get to answer by using that identity.. :P

Answer 29

use the identity :
sinP sinQ = -1/2 (cos(P+Q - cos(P-Q)
so, ur equation above can be like this :
sin(a+b)sin(a-b) = -1/2(cos2a - cos2b)

then use the identity :
cos2x = 1 - 2sin^2 x
so, that can simplied be
sin(a+b)sin(a-b) = -1/2(cos2a - cos2b)
= -1/2 (1-2sin^2 a - (1-2sin^2 b))
= -1/2 (-2sin^2 a + 2sin^2 b)
= sin^2 a - 2sin^2 b