Put s = sinx, c = cosx. Then (4-4s)(4+4s) =

16(1-s)(1+s) = 16(1-s^2) = 16c^2.

Remember that (a+b)(a-b) = a²-b² ..............[1]

..........(4 − 4 sin x)(4 + 4 sin x)

has the same format as (a+b)(a-b) if we let a = 4 and b = 4 sin x.

Using [1], we have

..........(4 − 4 sin x)(4 + 4 sin x) = 4² - (4 sin x)²

....................= 16-16 sin²x............ANS

........................// You can also simplify the answer

....................= 16(1- sin²x)............ANS

....................= 16 cos²x.................ANS

==> 16 - 16sin^2(x)

==> 16(1 - sin^2(x))

==> 16 cos^2(x)

(4 - 4sin(x)) (4 + 4sin(x)) = 4² - (4sin(x))²

= 16 - 16sin²(x)

= 16(1 - sin²(x)

= 16cos²(x)