simplify by expressing the product as a sum containing only

simplify by expressing the product as a sum containing only sines and cosines.

sin(4theta)sin(6theta)cos(4theta)cos(6theta)

Solution

Using sin 2x = 2sin x * cos x

sinA*sinB = 1/2*[cos(A-B) - cos(A+B)]

Given

sin(4)sin(6)*cos(4)cos(6)

= sin(4)cos(4) * sin(6)cos(6) = 1/4*sin(8)sin(12) = 1/8*[cos4 - cos20]