How do u change (-6sin(6x))/(cos^2(6x)+1) into -(12 sin(6x)) / (cos(12x) + 3)

how do u change (-6sin(6x))/(cos^2(6x)+1) into -(12 sin(6x)) / ((cos(12x) + 3) ?

They are equal!

Use the ID cos²Θ = 1/2 + (1/2)cos(2Θ). So cos²(6x) = (1/2) + (1/2)cos(12x). Then multiply numerator and denominator by 2 to clear the fractional part.

-6sin(6x)/(cos²(6x) + 1) = -6sin(6x)/(½cos(12x) + 3/2) = -12sin(6x)/(cos(12x) + 3).