Question

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prove sin2x - sin2y = sin(x + y)sin(x - y)?
✳️ brainlian give proper answer​

Answer 1

Answer:

R.H.S = sin(x+y) sin(x-y)

= (sin x cos y+ cos x siny) (sinx cosy- cosx siny)

= sin^2x cos^y- cos^x sin^y

= sin^2x(1-sin2y)-1(sin^2x) sin^2y

= sin^2x-sin^2x sin^2y-sin^y+sin^2x sin^2y

= sin^2x- sin^x sin^2y- sin^2y+sin^2x sin^2y

= sin^2x-sin^2y

= L.H.S

[proved]

Step-by-step explanation:

Hope it will help..

Answer 2

Lᴇᴛ ᴜs sᴛᴀʀᴛ ᴡɪᴛʜ RHS

sɪɴ(x+ʏ)sɪɴ(x−ʏ)

=(sɪɴxᴄᴏsʏ+ᴄᴏsxsɪɴʏ)(sɪɴxᴄᴏsʏ–ᴄᴏsxsɪɴʏ)

=(sɪɴ2xᴄᴏs2ʏ−ᴄᴏs2xsɪɴ2ʏ)

=sɪɴ2x(1−sɪɴ2ʏ)−(1−sɪɴ2x)sɪɴ2ʏ

=sɪɴ2−sɪɴ2ʏ

= LHS