Rewrite the sum as a product. sin(3x) + sin(7x)

Answer 1

sin(3x) + sin(7x)= sin(7x)+sin(3x)

Direct application of:

sin(a) + sin(b) = 2 sin((a+b)/2) * cos ((a-b)/2)

Set up a= 7x and b=3x

then simplify:

sin(7x) + sin(3x)= 2 sin ((7+3)/2)*cos((7-3)/2)

= 2 sin(5x) * cos(2x)

Answer 2

sin(3x) + sin(7x)

Using

Sin C + Sin D = 2 Sin ( C+ D)/2. Cos ( C-D)/2 = 2 Sin (3x + 7x)/ 2 . Cos (3x -7x)/2

= 2 Sin5x . Cos (-2x) = 2Sin5x . Cos 2x

(As Cos (-A ) = Cos A)