Question

Show that:(Class 11)
Sin (∝+Β) Cos(∝-Β) + Cos(∝+Β)Sin(∝-Β)= Sin2∝

Answer 1

Answer:

Sin( a + B ) = sin a cos B + cos a sinB

Cos ( a - B ) = cos a cos B + sina sin B

Cos ( a + B ) = cos a cos B - sin a sin B

Sin ( a - B ) = sin a cos B - cos a sin B

And sin 2 a = 2 sin a cos a

Now,

=> (sin a cos B + cos a sinB) (cos a cos B + sina sin B) + ( cos a cos B - sin a sin B) (sin a cos B - cos a sin B)

=> ( sin a cos a cos^2 B + sin^2 a sin B cos B + cos^2a sin B cos B + sin^2 B cos a sin a )

+ ( cos^2 B cos a sin a - cos^2a cos B sin B - sin^2 a sin B cos B + sin^2 B sin a cos a )

=> cos a sin a + cos a sin a

=> 2 sin a cos a

=> sin 2 a = RHS

QED

Answer 2

Answer:

hope it helps u........