Pls help to prove cos^2(2θ)-cos^2(6θ)=sin4θ*sin8θ. Thanks

sin(4theta)*sin(8theta)

We can use

cos(A)cos(B) - sin(A)sin(B)
if
we subtact these two

-2sin(A)sin(B)

so if and we
get

-2sin(8theta)sin(4theta)

-2sin(4theta)sin(8theta)

2sin(4theta)sin(8theta)

sin(4theta)sin(8theta)

cos^2(6theta) = sin(4theta)sin(8theta) = 1/2 (cos(4theta) - cos(12theta))
use the double angle formula

1

1/2(2cos^2(2theta) - 1 - (2cos^2(6theta))

1/2(2cos^2(2theta) - 1 - 2cos^2(6theta) + 1)

1/2(2cos^2(2theta) - 2cos^2(6theta))

cos^2(6theta)

This was what we wanted to
prove...