We have been given the following function:
f(x) = -4sin²(x)
By Pythagorean identity:
sin²x + cos²x = 1. Using this in the function given above:
f(x) = -4(1 - cos²x)
⇒f(x) = -4 + 4cos²x
By half angle identity:
cos²x = 1/2[1-cos(2x)]
Using this in the function above:
⇒f(x) = -4 + 4 (1/2[1-cos(2x)])
⇒f(x) = -4 + 2[1 - cos(2x)]
⇒f(x) = -4 + 2 -2cos(2x)
⇒f(x) = -2 -2cos(2x)
⇒f(x) = -2[1 + cos(2x)]
