Prove that:`cos^2 2x-cos^2 6x=sin4xsin8x`

Explanation

Here, we will use the following formulas,
`cosA+cosB = 2cos((A+B)/2)cos((A-B)/2)`

`cosA-cosB = -2sin((A+B)/2)sin((A-B)/2)`

`sin2x = 2sinxcosx`


`L.H.S. = cos^2(2x) - cos^2(6x)`

As, we know, `a^2-b^2 = (a+b)(a-b)`

So, `cos^2(2x) - cos^2(6x) = (cos2x+cos6x)(cos2x-cos6x)`

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