Simplify the expression by using a double-angle formula. 2 cos^2 4 theta -1

You are given 2cos² (4θ - 1). You are asked to simplify the expression by using a double-angle formula. 

Apply the double angle of the cosine function
cos2θ = 2cos² θ - 1

Rearranging the expression and then substituting them
2cos² θ = cos2θ + 1
2cos² (4θ - 1) = cos 2(4θ - 1) + 1
cos2(4θ - 1) + 1

The slope of the function is 0.5.