Question

Verifying identity plz help!Sin(x+y) sin(x-y)=sin²x-sin²y​

Answer 1

Answer:

Step-by-step explanation:

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

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

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

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

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

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

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

So L.H.S=R.H.S

Hence proved