Write the sum as a product sin 4x sin 2x 2 sin 4x 2x2 cos4

Write the sum as a product, sin 4x + sin 2x 2 sin (4x - 2x/2) cos(4x - 2x/2) Find the value of the product. 2 sin 52.5 sin 97.5

Solution

sinA+sinB=2sin((A+B)_/2)cos((A-B)_/2)

sin4x+sin2x=2sin((4x+2x)_/2)cos((4x-2x)_/2)

sin4x+sin2x=2sin((6x)_/2)cos((2x)_/2)

sin4x+sin2x=2sin(3x) cos(x)