Question

Prove the following:

${\text{cos}}^2$ 2x - ${\text{cos}}^2$ 6x = sin 4x sin 8x

Answer 1

We have,

L.H.S. = ${\text{cos}}^2$ 2x -${\text{cos}}^2$ 6x

= sin(6x+2x). sin(6x- 2x)

[$\because$ ${\text{cos}}^2$ B- ${\text{cos}}^2$ A =sin(A+B) sin(A-B)]

= sin 8x sin 4x = R.H.S.